{"backend_name": "ibm_brussels", "backend_version": "1.1.428", "n_qubits": 127, "basis_gates": ["ecr", "id", "rz", "sx", "x"], "gates": [{"name": "id", "parameters": [], "qasm_def": "gate id q { U(0, 0, 0) q; }", "coupling_map": [[0], [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], [22], [23], [24], [25], [26], [27], [28], [29], [30], [31], [32], [33], [34], [35], [36], [37], [38], [39], [40], [41], [42], [43], [44], [45], [46], [47], [48], [49], [50], [51], [52], [53], [54], [55], [56], [57], [58], [59], [60], [61], [62], [63], [64], [65], [66], [67], [68], [69], [70], [71], [72], [73], [74], [75], [76], [77], [78], [79], [80], [81], [82], [83], [84], [85], [86], [87], [88], [89], [90], [91], [92], [93], [94], [95], [96], [97], [98], [99], [100], [101], [102], [103], [104], [105], [106], [107], [108], [109], [110], [111], [112], [113], [114], [115], [116], [117], [118], [119], [120], [121], [122], [123], [124], [125], [126]]}, {"name": "rz", "parameters": ["theta"], "qasm_def": "gate rz(theta) q { U(0, 0, theta) q; }", "coupling_map": [[0], [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], [22], [23], [24], [25], [26], [27], [28], [29], [30], [31], [32], [33], [34], [35], [36], [37], [38], [39], [40], [41], [42], [43], [44], [45], [46], [47], [48], [49], [50], [51], [52], [53], [54], [55], [56], [57], [58], [59], [60], [61], [62], [63], [64], [65], [66], [67], [68], [69], [70], [71], [72], [73], [74], [75], [76], [77], [78], [79], [80], [81], [82], [83], [84], [85], [86], [87], [88], [89], [90], [91], [92], [93], [94], [95], [96], [97], [98], [99], [100], [101], [102], [103], [104], [105], [106], [107], [108], [109], [110], [111], [112], [113], [114], [115], [116], [117], [118], [119], [120], [121], [122], [123], [124], [125], [126]]}, {"name": "sx", "parameters": [], "qasm_def": "gate sx q { U(pi/2, 3*pi/2, pi/2) q; }", "coupling_map": [[0], [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], [22], [23], [24], [25], [26], [27], [28], [29], [30], [31], [32], [33], [34], [35], [36], [37], [38], [39], [40], [41], [42], [43], [44], [45], [46], [47], [48], [49], [50], [51], [52], [53], [54], [55], [56], [57], [58], [59], [60], [61], [62], [63], [64], [65], [66], [67], [68], [69], [70], [71], [72], [73], [74], [75], [76], [77], [78], [79], [80], [81], [82], [83], [84], [85], [86], [87], [88], [89], [90], [91], [92], [93], [94], [95], [96], [97], [98], [99], [100], [101], [102], [103], [104], [105], [106], [107], [108], [109], [110], [111], [112], [113], [114], [115], [116], [117], [118], [119], [120], [121], [122], [123], [124], [125], [126]]}, {"name": "x", "parameters": [], "qasm_def": "gate x q { U(pi, 0, pi) q; }", "coupling_map": [[0], [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], [22], [23], [24], [25], [26], [27], [28], [29], [30], [31], [32], [33], [34], [35], [36], [37], [38], [39], [40], [41], [42], [43], [44], [45], [46], [47], [48], [49], [50], [51], [52], [53], [54], [55], [56], [57], [58], [59], [60], [61], [62], [63], [64], [65], [66], [67], [68], [69], [70], [71], [72], [73], [74], [75], [76], [77], [78], [79], [80], [81], [82], [83], [84], [85], [86], [87], [88], [89], [90], [91], [92], [93], [94], [95], [96], [97], [98], [99], [100], [101], [102], [103], [104], [105], [106], [107], [108], [109], [110], [111], [112], [113], [114], [115], [116], [117], [118], [119], [120], [121], [122], [123], [124], [125], [126]]}, {"name": "ecr", "parameters": [], "qasm_def": "gate ecr q0, q1 { U(pi, pi/2, 7*pi/2) q0; U(pi, 7*pi/2, pi/2) q1; CX q0, q1; U(0, 0, 7*pi/2) q0; U(pi/2, 7*pi/2, pi/2) q1; }", "coupling_map": [[0, 1], [1, 2], [2, 3], [4, 3], [4, 15], [5, 4], [5, 6], [6, 7], [8, 7], [8, 9], [10, 9], [11, 10], [11, 12], [12, 17], [13, 12], [14, 0], [15, 22], [16, 8], [17, 30], [18, 14], [18, 19], [19, 20], [21, 20], [22, 21], [22, 23], [24, 23], [25, 24], [25, 26], [26, 16], [27, 26], [28, 27], [28, 29], [28, 35], [30, 29], [31, 30], [32, 31], [32, 36], [33, 20], [33, 39], [34, 24], [35, 47], [37, 38], [37, 52], [39, 38], [39, 40], [40, 41], [41, 42], [43, 34], [43, 42], [44, 43], [45, 44], [45, 54], [46, 45], [46, 47], [47, 48], [48, 49], [49, 50], [49, 55], [50, 51], [51, 36], [52, 56], [53, 41], [53, 60], [54, 64], [55, 68], [57, 56], [57, 58], [58, 59], [59, 60], [60, 61], [62, 61], [62, 72], [63, 62], [64, 63], [64, 65], [66, 65], [66, 73], [67, 66], [68, 67], [69, 68], [70, 69], [70, 74], [71, 58], [71, 77], [74, 89], [76, 75], [76, 77], [78, 77], [79, 78], [79, 80], [79, 91], [80, 81], [81, 72], [82, 81], [82, 83], [83, 92], [84, 83], [85, 73], [85, 84], [85, 86], [87, 86], [88, 87], [88, 89], [90, 75], [91, 98], [92, 102], [93, 87], [93, 106], [94, 90], [94, 95], [96, 95], [96, 97], [96, 109], [97, 98], [99, 98], [99, 100], [101, 100], [101, 102], [103, 102], [104, 103], [104, 111], [105, 104], [106, 105], [107, 106], [107, 108], [108, 112], [110, 100], [113, 114], [114, 109], [115, 114], [115, 116], [117, 116], [117, 118], [118, 110], [119, 118], [119, 120], [120, 121], [122, 111], [122, 121], [122, 123], [124, 123], [124, 125], [125, 126], [126, 112]]}, {"name": "reset", "parameters": [], "qasm_def": null}, {"name": "measure", "parameters": [], "qasm_def": null}], "local": false, "simulator": false, "conditional": false, "open_pulse": true, "memory": true, "coupling_map": [[0, 1], [1, 2], [2, 3], [4, 3], [4, 15], [5, 4], [5, 6], [6, 7], [8, 7], [8, 9], [10, 9], [11, 10], [11, 12], [12, 17], [13, 12], [14, 0], [15, 22], [16, 8], [17, 30], [18, 14], [18, 19], [19, 20], [21, 20], [22, 21], [22, 23], [24, 23], [25, 24], [25, 26], [26, 16], [27, 26], [28, 27], [28, 29], [28, 35], [30, 29], [31, 30], [32, 31], [32, 36], [33, 20], [33, 39], [34, 24], [35, 47], [37, 38], [37, 52], [39, 38], [39, 40], [40, 41], [41, 42], [43, 34], [43, 42], [44, 43], [45, 44], [45, 54], [46, 45], [46, 47], [47, 48], [48, 49], [49, 50], [49, 55], [50, 51], [51, 36], [52, 56], [53, 41], [53, 60], [54, 64], [55, 68], [57, 56], [57, 58], [58, 59], [59, 60], [60, 61], [62, 61], [62, 72], [63, 62], [64, 63], [64, 65], [66, 65], [66, 73], [67, 66], [68, 67], [69, 68], [70, 69], [70, 74], [71, 58], [71, 77], [74, 89], [76, 75], [76, 77], [78, 77], [79, 78], [79, 80], [79, 91], [80, 81], [81, 72], [82, 81], [82, 83], [83, 92], [84, 83], [85, 73], [85, 84], [85, 86], [87, 86], [88, 87], [88, 89], [90, 75], [91, 98], [92, 102], [93, 87], [93, 106], [94, 90], [94, 95], [96, 95], [96, 97], [96, 109], [97, 98], [99, 98], [99, 100], [101, 100], [101, 102], [103, 102], [104, 103], [104, 111], [105, 104], [106, 105], [107, 106], [107, 108], [108, 112], [110, 100], [113, 114], [114, 109], [115, 114], [115, 116], [117, 116], [117, 118], [118, 110], [119, 118], [119, 120], [120, 121], [122, 111], [122, 121], [122, 123], [124, 123], [124, 125], [125, 126], [126, 112]], "dynamic_reprate_enabled": true, "meas_levels": [1, 2], "meas_kernels": ["hw_qmfk"], "discriminators": ["hw_qmfk", "quadratic_discriminator", "linear_discriminator"], "meas_map": [[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126]], "supported_instructions": ["id", "if_else", "reset", "ecr", "delay", "sx", "store", "acquire", "rz", "setf", "measure", "play", "u1", "shiftf", "x"], "rep_delay_range": [0.0, 2000.0], "default_rep_delay": 250.0, "sample_name": "family: Eagle, revision: 3", "n_registers": 1, "credits_required": true, "online_date": "2024-03-14T23:00:00+00:00", "description": "127 qubit device", "dt": 4.0, "dtm": 4.0, "processor_type": {"family": "Eagle", "revision": 3}, "parametric_pulses": ["gaussian", "gaussian_square", "gaussian_square_drag", "drag", "constant"], "acquisition_latency": [], "allow_q_object": true, "channels": {"acquire0": {"operates": {"qubits": [0]}, "purpose": "acquire", "type": "acquire"}, "acquire1": {"operates": {"qubits": [1]}, "purpose": "acquire", "type": "acquire"}, "acquire10": {"operates": {"qubits": [10]}, "purpose": "acquire", "type": "acquire"}, "acquire100": {"operates": {"qubits": [100]}, "purpose": "acquire", "type": "acquire"}, "acquire101": {"operates": {"qubits": [101]}, "purpose": "acquire", "type": "acquire"}, "acquire102": {"operates": {"qubits": [102]}, "purpose": "acquire", "type": "acquire"}, "acquire103": {"operates": {"qubits": [103]}, "purpose": "acquire", "type": "acquire"}, "acquire104": {"operates": {"qubits": [104]}, "purpose": "acquire", "type": "acquire"}, "acquire105": {"operates": {"qubits": [105]}, "purpose": "acquire", "type": "acquire"}, "acquire106": {"operates": {"qubits": [106]}, "purpose": "acquire", "type": "acquire"}, "acquire107": {"operates": {"qubits": [107]}, "purpose": "acquire", "type": "acquire"}, "acquire108": {"operates": {"qubits": [108]}, "purpose": "acquire", "type": "acquire"}, "acquire109": {"operates": {"qubits": [109]}, "purpose": "acquire", "type": "acquire"}, "acquire11": {"operates": {"qubits": [11]}, "purpose": "acquire", "type": "acquire"}, "acquire110": {"operates": {"qubits": [110]}, "purpose": "acquire", "type": "acquire"}, "acquire111": {"operates": {"qubits": [111]}, "purpose": "acquire", "type": "acquire"}, "acquire112": {"operates": {"qubits": [112]}, "purpose": "acquire", "type": "acquire"}, "acquire113": {"operates": {"qubits": [113]}, "purpose": "acquire", "type": "acquire"}, "acquire114": {"operates": {"qubits": [114]}, "purpose": "acquire", "type": "acquire"}, "acquire115": {"operates": {"qubits": [115]}, "purpose": "acquire", "type": "acquire"}, "acquire116": {"operates": {"qubits": [116]}, "purpose": "acquire", "type": "acquire"}, "acquire117": {"operates": {"qubits": [117]}, "purpose": "acquire", "type": "acquire"}, "acquire118": {"operates": {"qubits": [118]}, "purpose": "acquire", "type": "acquire"}, "acquire119": {"operates": {"qubits": [119]}, "purpose": "acquire", "type": "acquire"}, "acquire12": {"operates": {"qubits": [12]}, "purpose": "acquire", "type": "acquire"}, "acquire120": {"operates": {"qubits": [120]}, "purpose": "acquire", "type": "acquire"}, "acquire121": {"operates": {"qubits": [121]}, "purpose": "acquire", "type": "acquire"}, "acquire122": {"operates": {"qubits": [122]}, "purpose": "acquire", "type": "acquire"}, "acquire123": {"operates": {"qubits": [123]}, "purpose": "acquire", "type": "acquire"}, "acquire124": {"operates": {"qubits": [124]}, "purpose": "acquire", "type": "acquire"}, "acquire125": {"operates": {"qubits": [125]}, "purpose": "acquire", "type": "acquire"}, "acquire126": {"operates": {"qubits": [126]}, "purpose": "acquire", "type": "acquire"}, "acquire13": {"operates": {"qubits": [13]}, "purpose": "acquire", "type": "acquire"}, "acquire14": {"operates": {"qubits": [14]}, "purpose": "acquire", "type": "acquire"}, "acquire15": {"operates": {"qubits": [15]}, "purpose": "acquire", "type": "acquire"}, "acquire16": {"operates": {"qubits": [16]}, "purpose": "acquire", "type": "acquire"}, "acquire17": {"operates": {"qubits": [17]}, "purpose": "acquire", "type": "acquire"}, "acquire18": {"operates": {"qubits": [18]}, "purpose": "acquire", "type": "acquire"}, "acquire19": {"operates": {"qubits": [19]}, "purpose": "acquire", "type": "acquire"}, "acquire2": {"operates": {"qubits": [2]}, "purpose": "acquire", "type": "acquire"}, "acquire20": {"operates": {"qubits": [20]}, "purpose": "acquire", "type": "acquire"}, "acquire21": {"operates": {"qubits": [21]}, "purpose": "acquire", "type": "acquire"}, "acquire22": {"operates": {"qubits": [22]}, "purpose": "acquire", "type": "acquire"}, "acquire23": {"operates": {"qubits": [23]}, "purpose": "acquire", "type": "acquire"}, "acquire24": {"operates": {"qubits": [24]}, "purpose": "acquire", "type": "acquire"}, "acquire25": {"operates": {"qubits": [25]}, "purpose": "acquire", "type": "acquire"}, "acquire26": {"operates": {"qubits": [26]}, "purpose": "acquire", "type": "acquire"}, "acquire27": {"operates": {"qubits": [27]}, "purpose": "acquire", "type": "acquire"}, "acquire28": {"operates": {"qubits": [28]}, "purpose": "acquire", "type": "acquire"}, "acquire29": {"operates": {"qubits": [29]}, "purpose": "acquire", "type": "acquire"}, "acquire3": {"operates": {"qubits": [3]}, "purpose": "acquire", "type": "acquire"}, "acquire30": {"operates": {"qubits": [30]}, "purpose": "acquire", "type": "acquire"}, "acquire31": {"operates": {"qubits": [31]}, "purpose": "acquire", "type": "acquire"}, "acquire32": {"operates": {"qubits": [32]}, "purpose": "acquire", "type": "acquire"}, "acquire33": {"operates": {"qubits": [33]}, "purpose": "acquire", "type": "acquire"}, "acquire34": {"operates": {"qubits": [34]}, "purpose": "acquire", "type": "acquire"}, "acquire35": {"operates": {"qubits": [35]}, "purpose": "acquire", "type": "acquire"}, "acquire36": {"operates": {"qubits": [36]}, "purpose": "acquire", "type": "acquire"}, "acquire37": {"operates": {"qubits": [37]}, "purpose": "acquire", "type": "acquire"}, "acquire38": {"operates": {"qubits": [38]}, "purpose": "acquire", "type": "acquire"}, "acquire39": {"operates": {"qubits": [39]}, "purpose": "acquire", "type": "acquire"}, "acquire4": {"operates": {"qubits": [4]}, "purpose": "acquire", "type": "acquire"}, "acquire40": {"operates": {"qubits": [40]}, "purpose": "acquire", "type": "acquire"}, "acquire41": {"operates": {"qubits": [41]}, "purpose": "acquire", "type": "acquire"}, "acquire42": {"operates": {"qubits": [42]}, "purpose": "acquire", "type": "acquire"}, "acquire43": {"operates": {"qubits": [43]}, "purpose": "acquire", "type": "acquire"}, "acquire44": {"operates": {"qubits": [44]}, "purpose": "acquire", "type": "acquire"}, "acquire45": {"operates": {"qubits": [45]}, "purpose": "acquire", "type": "acquire"}, "acquire46": {"operates": {"qubits": [46]}, "purpose": "acquire", "type": "acquire"}, "acquire47": {"operates": {"qubits": [47]}, "purpose": "acquire", "type": "acquire"}, "acquire48": {"operates": {"qubits": [48]}, "purpose": "acquire", "type": "acquire"}, "acquire49": {"operates": {"qubits": [49]}, "purpose": "acquire", "type": "acquire"}, "acquire5": {"operates": {"qubits": [5]}, "purpose": "acquire", "type": "acquire"}, "acquire50": {"operates": {"qubits": [50]}, "purpose": "acquire", "type": "acquire"}, "acquire51": {"operates": {"qubits": [51]}, "purpose": "acquire", "type": "acquire"}, "acquire52": {"operates": {"qubits": [52]}, "purpose": "acquire", "type": "acquire"}, "acquire53": {"operates": {"qubits": [53]}, "purpose": "acquire", "type": "acquire"}, "acquire54": {"operates": {"qubits": [54]}, "purpose": "acquire", "type": "acquire"}, "acquire55": {"operates": {"qubits": [55]}, "purpose": "acquire", "type": "acquire"}, "acquire56": {"operates": {"qubits": [56]}, "purpose": "acquire", "type": "acquire"}, "acquire57": {"operates": {"qubits": [57]}, "purpose": "acquire", "type": "acquire"}, "acquire58": {"operates": {"qubits": [58]}, "purpose": "acquire", "type": "acquire"}, "acquire59": {"operates": {"qubits": [59]}, "purpose": "acquire", "type": "acquire"}, "acquire6": {"operates": {"qubits": [6]}, "purpose": "acquire", "type": "acquire"}, "acquire60": {"operates": {"qubits": [60]}, "purpose": "acquire", "type": "acquire"}, "acquire61": {"operates": {"qubits": [61]}, "purpose": "acquire", "type": "acquire"}, "acquire62": {"operates": {"qubits": [62]}, "purpose": "acquire", "type": "acquire"}, "acquire63": {"operates": {"qubits": [63]}, "purpose": "acquire", "type": "acquire"}, "acquire64": {"operates": {"qubits": [64]}, "purpose": "acquire", "type": "acquire"}, "acquire65": {"operates": {"qubits": [65]}, "purpose": "acquire", "type": "acquire"}, "acquire66": {"operates": {"qubits": [66]}, "purpose": "acquire", "type": "acquire"}, "acquire67": {"operates": {"qubits": [67]}, "purpose": "acquire", "type": "acquire"}, "acquire68": {"operates": {"qubits": [68]}, "purpose": "acquire", "type": "acquire"}, "acquire69": {"operates": {"qubits": [69]}, "purpose": "acquire", "type": "acquire"}, "acquire7": {"operates": {"qubits": [7]}, "purpose": "acquire", "type": "acquire"}, "acquire70": {"operates": {"qubits": [70]}, "purpose": "acquire", "type": "acquire"}, "acquire71": {"operates": {"qubits": [71]}, "purpose": "acquire", "type": "acquire"}, "acquire72": {"operates": {"qubits": [72]}, "purpose": "acquire", "type": "acquire"}, "acquire73": {"operates": {"qubits": [73]}, "purpose": "acquire", "type": "acquire"}, "acquire74": {"operates": {"qubits": [74]}, "purpose": "acquire", "type": "acquire"}, "acquire75": {"operates": {"qubits": [75]}, "purpose": "acquire", "type": "acquire"}, "acquire76": {"operates": {"qubits": [76]}, "purpose": "acquire", "type": "acquire"}, "acquire77": {"operates": {"qubits": [77]}, "purpose": "acquire", "type": "acquire"}, "acquire78": {"operates": {"qubits": [78]}, "purpose": "acquire", "type": "acquire"}, "acquire79": {"operates": {"qubits": [79]}, "purpose": "acquire", "type": "acquire"}, "acquire8": {"operates": {"qubits": [8]}, "purpose": "acquire", "type": "acquire"}, "acquire80": {"operates": {"qubits": [80]}, "purpose": "acquire", "type": "acquire"}, "acquire81": {"operates": {"qubits": [81]}, "purpose": "acquire", "type": "acquire"}, "acquire82": {"operates": {"qubits": [82]}, "purpose": "acquire", "type": "acquire"}, "acquire83": {"operates": {"qubits": [83]}, "purpose": "acquire", "type": "acquire"}, "acquire84": {"operates": {"qubits": [84]}, "purpose": "acquire", "type": "acquire"}, "acquire85": 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[50, 49]}, "purpose": "cross-resonance", "type": "control"}, "u115": {"operates": {"qubits": [50, 51]}, "purpose": "cross-resonance", "type": "control"}, "u116": {"operates": {"qubits": [51, 36]}, "purpose": "cross-resonance", "type": "control"}, "u117": {"operates": {"qubits": [51, 50]}, "purpose": "cross-resonance", "type": "control"}, "u118": {"operates": {"qubits": [52, 37]}, "purpose": "cross-resonance", "type": "control"}, "u119": {"operates": {"qubits": [52, 56]}, "purpose": "cross-resonance", "type": "control"}, "u12": {"operates": {"qubits": [5, 6]}, "purpose": "cross-resonance", "type": "control"}, "u120": {"operates": {"qubits": [53, 41]}, "purpose": "cross-resonance", "type": "control"}, "u121": {"operates": {"qubits": [53, 60]}, "purpose": "cross-resonance", "type": "control"}, "u122": {"operates": {"qubits": [54, 45]}, "purpose": "cross-resonance", "type": "control"}, "u123": {"operates": {"qubits": [54, 64]}, "purpose": "cross-resonance", "type": "control"}, "u124": {"operates": {"qubits": [55, 49]}, "purpose": "cross-resonance", "type": "control"}, "u125": {"operates": {"qubits": [55, 68]}, "purpose": "cross-resonance", "type": "control"}, "u126": {"operates": {"qubits": [56, 52]}, "purpose": "cross-resonance", "type": "control"}, "u127": {"operates": {"qubits": [56, 57]}, "purpose": "cross-resonance", "type": "control"}, "u128": {"operates": {"qubits": [57, 56]}, "purpose": "cross-resonance", "type": "control"}, "u129": {"operates": {"qubits": [57, 58]}, "purpose": "cross-resonance", "type": "control"}, "u13": {"operates": {"qubits": [6, 5]}, "purpose": "cross-resonance", "type": "control"}, "u130": {"operates": {"qubits": [58, 57]}, "purpose": "cross-resonance", "type": "control"}, "u131": {"operates": {"qubits": [58, 59]}, "purpose": "cross-resonance", "type": "control"}, "u132": {"operates": {"qubits": [58, 71]}, "purpose": "cross-resonance", "type": "control"}, "u133": {"operates": {"qubits": [59, 58]}, "purpose": "cross-resonance", "type": 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"cross-resonance", "type": "control"}, "u144": {"operates": {"qubits": [63, 64]}, "purpose": "cross-resonance", "type": "control"}, "u145": {"operates": {"qubits": [64, 54]}, "purpose": "cross-resonance", "type": "control"}, "u146": {"operates": {"qubits": [64, 63]}, "purpose": "cross-resonance", "type": "control"}, "u147": {"operates": {"qubits": [64, 65]}, "purpose": "cross-resonance", "type": "control"}, "u148": {"operates": {"qubits": [65, 64]}, "purpose": "cross-resonance", "type": "control"}, "u149": {"operates": {"qubits": [65, 66]}, "purpose": "cross-resonance", "type": "control"}, "u15": {"operates": {"qubits": [7, 6]}, "purpose": "cross-resonance", "type": "control"}, "u150": {"operates": {"qubits": [66, 65]}, "purpose": "cross-resonance", "type": "control"}, "u151": {"operates": {"qubits": [66, 67]}, "purpose": "cross-resonance", "type": "control"}, "u152": {"operates": {"qubits": [66, 73]}, "purpose": "cross-resonance", "type": "control"}, "u153": {"operates": {"qubits": [67, 66]}, "purpose": "cross-resonance", "type": "control"}, "u154": {"operates": {"qubits": [67, 68]}, "purpose": "cross-resonance", "type": "control"}, "u155": {"operates": {"qubits": [68, 55]}, "purpose": "cross-resonance", "type": "control"}, "u156": {"operates": {"qubits": [68, 67]}, "purpose": "cross-resonance", "type": "control"}, "u157": {"operates": {"qubits": [68, 69]}, "purpose": "cross-resonance", "type": "control"}, "u158": {"operates": {"qubits": [69, 68]}, "purpose": "cross-resonance", "type": "control"}, "u159": {"operates": {"qubits": [69, 70]}, "purpose": "cross-resonance", "type": "control"}, "u16": {"operates": {"qubits": [7, 8]}, "purpose": "cross-resonance", "type": "control"}, "u160": {"operates": {"qubits": [70, 69]}, "purpose": "cross-resonance", "type": "control"}, "u161": {"operates": {"qubits": [70, 74]}, "purpose": "cross-resonance", "type": "control"}, "u162": {"operates": {"qubits": [71, 58]}, "purpose": "cross-resonance", "type": "control"}, "u163": {"operates": {"qubits": [71, 77]}, "purpose": "cross-resonance", "type": "control"}, "u164": {"operates": {"qubits": [72, 62]}, "purpose": "cross-resonance", "type": "control"}, "u165": {"operates": {"qubits": [72, 81]}, "purpose": "cross-resonance", "type": "control"}, "u166": {"operates": {"qubits": [73, 66]}, "purpose": "cross-resonance", "type": "control"}, "u167": {"operates": {"qubits": [73, 85]}, "purpose": "cross-resonance", "type": "control"}, "u168": {"operates": {"qubits": [74, 70]}, "purpose": "cross-resonance", "type": "control"}, "u169": {"operates": {"qubits": [74, 89]}, "purpose": "cross-resonance", "type": "control"}, "u17": {"operates": {"qubits": [8, 7]}, "purpose": "cross-resonance", "type": "control"}, "u170": {"operates": {"qubits": [75, 76]}, "purpose": "cross-resonance", "type": "control"}, "u171": {"operates": {"qubits": [75, 90]}, "purpose": "cross-resonance", "type": "control"}, "u172": {"operates": {"qubits": [76, 75]}, "purpose": "cross-resonance", "type": 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[84, 83]}, "purpose": "cross-resonance", "type": "control"}, "u193": {"operates": {"qubits": [84, 85]}, "purpose": "cross-resonance", "type": "control"}, "u194": {"operates": {"qubits": [85, 73]}, "purpose": "cross-resonance", "type": "control"}, "u195": {"operates": {"qubits": [85, 84]}, "purpose": "cross-resonance", "type": "control"}, "u196": {"operates": {"qubits": [85, 86]}, "purpose": "cross-resonance", "type": "control"}, "u197": {"operates": {"qubits": [86, 85]}, "purpose": "cross-resonance", "type": "control"}, "u198": {"operates": {"qubits": [86, 87]}, "purpose": "cross-resonance", "type": "control"}, "u199": {"operates": {"qubits": [87, 86]}, "purpose": "cross-resonance", "type": "control"}, "u2": {"operates": {"qubits": [1, 0]}, "purpose": "cross-resonance", "type": "control"}, "u20": {"operates": {"qubits": [9, 8]}, "purpose": "cross-resonance", "type": "control"}, "u200": {"operates": {"qubits": [87, 88]}, "purpose": "cross-resonance", "type": "control"}, "u201": {"operates": {"qubits": [87, 93]}, "purpose": "cross-resonance", "type": "control"}, "u202": {"operates": {"qubits": [88, 87]}, "purpose": "cross-resonance", "type": "control"}, "u203": {"operates": {"qubits": [88, 89]}, "purpose": "cross-resonance", "type": "control"}, "u204": {"operates": {"qubits": [89, 74]}, "purpose": "cross-resonance", "type": "control"}, "u205": {"operates": {"qubits": [89, 88]}, "purpose": "cross-resonance", "type": "control"}, "u206": {"operates": {"qubits": [90, 75]}, "purpose": "cross-resonance", "type": "control"}, "u207": {"operates": {"qubits": [90, 94]}, "purpose": "cross-resonance", "type": "control"}, "u208": {"operates": {"qubits": [91, 79]}, "purpose": "cross-resonance", "type": "control"}, "u209": {"operates": {"qubits": [91, 98]}, "purpose": "cross-resonance", "type": "control"}, "u21": {"operates": {"qubits": [9, 10]}, "purpose": "cross-resonance", "type": "control"}, "u210": {"operates": {"qubits": [92, 83]}, "purpose": "cross-resonance", "type": "control"}, "u211": {"operates": {"qubits": [92, 102]}, "purpose": "cross-resonance", "type": "control"}, "u212": {"operates": {"qubits": [93, 87]}, "purpose": "cross-resonance", "type": "control"}, "u213": {"operates": {"qubits": [93, 106]}, "purpose": "cross-resonance", "type": "control"}, "u214": {"operates": {"qubits": [94, 90]}, "purpose": "cross-resonance", "type": "control"}, "u215": {"operates": {"qubits": [94, 95]}, "purpose": "cross-resonance", "type": "control"}, "u216": {"operates": {"qubits": [95, 94]}, "purpose": "cross-resonance", "type": "control"}, "u217": {"operates": {"qubits": [95, 96]}, "purpose": "cross-resonance", "type": "control"}, "u218": {"operates": {"qubits": [96, 95]}, "purpose": "cross-resonance", "type": "control"}, "u219": {"operates": {"qubits": [96, 97]}, "purpose": "cross-resonance", "type": "control"}, "u22": {"operates": {"qubits": [10, 9]}, "purpose": "cross-resonance", "type": "control"}, "u220": {"operates": {"qubits": [96, 109]}, "purpose": 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{"qubits": [100, 110]}, "purpose": "cross-resonance", "type": "control"}, "u231": {"operates": {"qubits": [101, 100]}, "purpose": "cross-resonance", "type": "control"}, "u232": {"operates": {"qubits": [101, 102]}, "purpose": "cross-resonance", "type": "control"}, "u233": {"operates": {"qubits": [102, 92]}, "purpose": "cross-resonance", "type": "control"}, "u234": {"operates": {"qubits": [102, 101]}, "purpose": "cross-resonance", "type": "control"}, "u235": {"operates": {"qubits": [102, 103]}, "purpose": "cross-resonance", "type": "control"}, "u236": {"operates": {"qubits": [103, 102]}, "purpose": "cross-resonance", "type": "control"}, "u237": {"operates": {"qubits": [103, 104]}, "purpose": "cross-resonance", "type": "control"}, "u238": {"operates": {"qubits": [104, 103]}, "purpose": "cross-resonance", "type": "control"}, "u239": {"operates": {"qubits": [104, 105]}, "purpose": "cross-resonance", "type": "control"}, "u24": {"operates": {"qubits": [11, 10]}, "purpose": "cross-resonance", "type": "control"}, "u240": {"operates": {"qubits": [104, 111]}, "purpose": "cross-resonance", "type": "control"}, "u241": {"operates": {"qubits": [105, 104]}, "purpose": "cross-resonance", "type": "control"}, "u242": {"operates": {"qubits": [105, 106]}, "purpose": "cross-resonance", "type": "control"}, "u243": {"operates": {"qubits": [106, 93]}, "purpose": "cross-resonance", "type": "control"}, "u244": {"operates": {"qubits": [106, 105]}, "purpose": "cross-resonance", "type": "control"}, "u245": {"operates": {"qubits": [106, 107]}, "purpose": "cross-resonance", "type": "control"}, "u246": {"operates": {"qubits": [107, 106]}, "purpose": "cross-resonance", "type": "control"}, "u247": {"operates": {"qubits": [107, 108]}, "purpose": "cross-resonance", "type": "control"}, "u248": {"operates": {"qubits": [108, 107]}, "purpose": "cross-resonance", "type": "control"}, "u249": {"operates": {"qubits": [108, 112]}, "purpose": "cross-resonance", "type": "control"}, "u25": {"operates": {"qubits": [11, 12]}, "purpose": "cross-resonance", "type": "control"}, "u250": {"operates": {"qubits": [109, 96]}, "purpose": "cross-resonance", "type": "control"}, "u251": {"operates": {"qubits": [109, 114]}, "purpose": "cross-resonance", "type": "control"}, "u252": {"operates": {"qubits": [110, 100]}, "purpose": "cross-resonance", "type": "control"}, "u253": {"operates": {"qubits": [110, 118]}, "purpose": "cross-resonance", "type": "control"}, "u254": {"operates": {"qubits": [111, 104]}, "purpose": "cross-resonance", "type": "control"}, "u255": {"operates": {"qubits": [111, 122]}, "purpose": "cross-resonance", "type": "control"}, "u256": {"operates": {"qubits": [112, 108]}, "purpose": "cross-resonance", "type": "control"}, "u257": {"operates": {"qubits": [112, 126]}, "purpose": "cross-resonance", "type": "control"}, "u258": {"operates": {"qubits": [113, 114]}, "purpose": "cross-resonance", "type": "control"}, "u259": {"operates": {"qubits": [114, 109]}, "purpose": "cross-resonance", "type": "control"}, "u26": {"operates": {"qubits": [12, 11]}, "purpose": "cross-resonance", "type": "control"}, "u260": {"operates": {"qubits": [114, 113]}, "purpose": "cross-resonance", "type": "control"}, "u261": {"operates": {"qubits": [114, 115]}, "purpose": "cross-resonance", "type": "control"}, "u262": {"operates": {"qubits": [115, 114]}, "purpose": "cross-resonance", "type": "control"}, "u263": {"operates": {"qubits": [115, 116]}, "purpose": "cross-resonance", "type": "control"}, "u264": {"operates": {"qubits": [116, 115]}, "purpose": "cross-resonance", "type": "control"}, "u265": {"operates": {"qubits": [116, 117]}, "purpose": "cross-resonance", "type": "control"}, "u266": {"operates": {"qubits": [117, 116]}, "purpose": "cross-resonance", "type": "control"}, "u267": {"operates": {"qubits": [117, 118]}, "purpose": "cross-resonance", "type": "control"}, "u268": {"operates": {"qubits": [118, 110]}, "purpose": "cross-resonance", "type": "control"}, "u269": {"operates": {"qubits": [118, 117]}, "purpose": "cross-resonance", "type": "control"}, "u27": {"operates": {"qubits": [12, 13]}, "purpose": "cross-resonance", "type": "control"}, "u270": {"operates": {"qubits": [118, 119]}, "purpose": "cross-resonance", "type": "control"}, "u271": {"operates": {"qubits": [119, 118]}, "purpose": "cross-resonance", "type": "control"}, "u272": {"operates": {"qubits": [119, 120]}, "purpose": "cross-resonance", "type": "control"}, "u273": {"operates": {"qubits": [120, 119]}, "purpose": "cross-resonance", "type": "control"}, "u274": {"operates": {"qubits": [120, 121]}, "purpose": "cross-resonance", "type": "control"}, "u275": {"operates": {"qubits": [121, 120]}, "purpose": "cross-resonance", "type": "control"}, "u276": {"operates": {"qubits": [121, 122]}, "purpose": "cross-resonance", "type": "control"}, "u277": {"operates": {"qubits": [122, 111]}, "purpose": "cross-resonance", "type": "control"}, "u278": {"operates": {"qubits": [122, 121]}, "purpose": "cross-resonance", "type": "control"}, "u279": {"operates": {"qubits": [122, 123]}, "purpose": "cross-resonance", "type": "control"}, "u28": {"operates": {"qubits": [12, 17]}, "purpose": "cross-resonance", "type": "control"}, "u280": {"operates": {"qubits": [123, 122]}, "purpose": "cross-resonance", "type": "control"}, "u281": {"operates": {"qubits": [123, 124]}, "purpose": "cross-resonance", "type": "control"}, "u282": {"operates": {"qubits": [124, 123]}, "purpose": "cross-resonance", "type": "control"}, "u283": {"operates": {"qubits": [124, 125]}, "purpose": "cross-resonance", "type": "control"}, "u284": {"operates": {"qubits": [125, 124]}, "purpose": "cross-resonance", "type": "control"}, "u285": {"operates": {"qubits": [125, 126]}, "purpose": "cross-resonance", "type": "control"}, "u286": {"operates": {"qubits": [126, 112]}, "purpose": "cross-resonance", "type": "control"}, "u287": {"operates": {"qubits": [126, 125]}, "purpose": "cross-resonance", "type": "control"}, "u29": {"operates": {"qubits": [13, 12]}, "purpose": "cross-resonance", "type": "control"}, "u3": {"operates": {"qubits": [1, 2]}, "purpose": "cross-resonance", "type": "control"}, "u30": {"operates": {"qubits": [14, 0]}, "purpose": "cross-resonance", "type": "control"}, "u31": {"operates": {"qubits": [14, 18]}, "purpose": "cross-resonance", "type": "control"}, "u32": {"operates": {"qubits": [15, 4]}, "purpose": "cross-resonance", "type": "control"}, "u33": {"operates": {"qubits": [15, 22]}, "purpose": "cross-resonance", "type": "control"}, "u34": {"operates": {"qubits": [16, 8]}, "purpose": "cross-resonance", "type": "control"}, "u35": {"operates": {"qubits": [16, 26]}, "purpose": "cross-resonance", "type": "control"}, "u36": {"operates": {"qubits": [17, 12]}, "purpose": "cross-resonance", "type": "control"}, "u37": {"operates": {"qubits": [17, 30]}, "purpose": "cross-resonance", "type": "control"}, "u38": {"operates": {"qubits": [18, 14]}, "purpose": "cross-resonance", "type": "control"}, "u39": {"operates": {"qubits": [18, 19]}, "purpose": "cross-resonance", "type": "control"}, "u4": {"operates": {"qubits": [2, 1]}, "purpose": "cross-resonance", "type": "control"}, "u40": {"operates": {"qubits": [19, 18]}, "purpose": "cross-resonance", "type": "control"}, "u41": {"operates": {"qubits": [19, 20]}, "purpose": "cross-resonance", "type": "control"}, "u42": {"operates": {"qubits": [20, 19]}, "purpose": "cross-resonance", "type": "control"}, "u43": {"operates": {"qubits": [20, 21]}, "purpose": "cross-resonance", "type": "control"}, "u44": {"operates": {"qubits": [20, 33]}, "purpose": "cross-resonance", "type": "control"}, "u45": {"operates": {"qubits": [21, 20]}, "purpose": "cross-resonance", "type": "control"}, "u46": {"operates": {"qubits": [21, 22]}, "purpose": "cross-resonance", "type": "control"}, "u47": {"operates": {"qubits": [22, 15]}, "purpose": "cross-resonance", "type": "control"}, "u48": {"operates": {"qubits": [22, 21]}, "purpose": "cross-resonance", "type": "control"}, "u49": {"operates": {"qubits": [22, 23]}, "purpose": "cross-resonance", "type": "control"}, "u5": {"operates": {"qubits": [2, 3]}, "purpose": "cross-resonance", "type": "control"}, "u50": {"operates": {"qubits": [23, 22]}, "purpose": "cross-resonance", "type": "control"}, "u51": {"operates": {"qubits": [23, 24]}, "purpose": "cross-resonance", "type": "control"}, "u52": {"operates": {"qubits": [24, 23]}, "purpose": "cross-resonance", "type": "control"}, "u53": {"operates": {"qubits": [24, 25]}, "purpose": "cross-resonance", "type": "control"}, "u54": {"operates": {"qubits": [24, 34]}, "purpose": "cross-resonance", "type": "control"}, "u55": {"operates": {"qubits": [25, 24]}, "purpose": "cross-resonance", "type": "control"}, "u56": {"operates": {"qubits": [25, 26]}, "purpose": "cross-resonance", "type": "control"}, "u57": {"operates": {"qubits": [26, 16]}, "purpose": "cross-resonance", "type": "control"}, "u58": {"operates": {"qubits": [26, 25]}, "purpose": "cross-resonance", "type": "control"}, "u59": {"operates": {"qubits": [26, 27]}, "purpose": "cross-resonance", "type": "control"}, "u6": {"operates": {"qubits": [3, 2]}, "purpose": "cross-resonance", "type": "control"}, "u60": {"operates": {"qubits": [27, 26]}, "purpose": "cross-resonance", "type": "control"}, "u61": {"operates": {"qubits": [27, 28]}, "purpose": "cross-resonance", "type": "control"}, "u62": {"operates": {"qubits": [28, 27]}, "purpose": "cross-resonance", "type": "control"}, "u63": {"operates": {"qubits": [28, 29]}, "purpose": "cross-resonance", "type": "control"}, "u64": {"operates": {"qubits": [28, 35]}, "purpose": "cross-resonance", "type": "control"}, "u65": {"operates": {"qubits": [29, 28]}, "purpose": "cross-resonance", "type": "control"}, "u66": {"operates": {"qubits": [29, 30]}, "purpose": "cross-resonance", "type": "control"}, "u67": {"operates": {"qubits": [30, 17]}, "purpose": "cross-resonance", "type": "control"}, "u68": {"operates": {"qubits": [30, 29]}, "purpose": "cross-resonance", "type": "control"}, "u69": {"operates": {"qubits": [30, 31]}, "purpose": "cross-resonance", "type": "control"}, "u7": {"operates": {"qubits": [3, 4]}, "purpose": "cross-resonance", "type": "control"}, "u70": {"operates": {"qubits": [31, 30]}, "purpose": "cross-resonance", "type": "control"}, "u71": {"operates": {"qubits": [31, 32]}, "purpose": "cross-resonance", "type": "control"}, "u72": {"operates": {"qubits": [32, 31]}, "purpose": "cross-resonance", "type": "control"}, "u73": {"operates": {"qubits": [32, 36]}, "purpose": "cross-resonance", "type": "control"}, "u74": {"operates": {"qubits": [33, 20]}, "purpose": "cross-resonance", "type": "control"}, "u75": {"operates": {"qubits": [33, 39]}, "purpose": "cross-resonance", "type": "control"}, "u76": {"operates": {"qubits": [34, 24]}, "purpose": "cross-resonance", "type": "control"}, "u77": {"operates": {"qubits": [34, 43]}, "purpose": "cross-resonance", "type": "control"}, "u78": {"operates": {"qubits": [35, 28]}, "purpose": "cross-resonance", "type": "control"}, "u79": {"operates": {"qubits": [35, 47]}, "purpose": "cross-resonance", "type": "control"}, "u8": {"operates": {"qubits": [4, 3]}, "purpose": "cross-resonance", "type": "control"}, "u80": {"operates": {"qubits": [36, 32]}, "purpose": "cross-resonance", "type": "control"}, "u81": {"operates": {"qubits": [36, 51]}, "purpose": "cross-resonance", "type": "control"}, "u82": {"operates": {"qubits": [37, 38]}, "purpose": "cross-resonance", "type": "control"}, "u83": {"operates": {"qubits": [37, 52]}, "purpose": "cross-resonance", "type": "control"}, "u84": {"operates": {"qubits": [38, 37]}, "purpose": "cross-resonance", "type": "control"}, "u85": {"operates": {"qubits": [38, 39]}, "purpose": "cross-resonance", "type": "control"}, "u86": {"operates": {"qubits": [39, 33]}, "purpose": "cross-resonance", "type": "control"}, "u87": {"operates": {"qubits": [39, 38]}, "purpose": "cross-resonance", "type": "control"}, "u88": {"operates": {"qubits": [39, 40]}, "purpose": "cross-resonance", "type": "control"}, "u89": {"operates": {"qubits": [40, 39]}, "purpose": "cross-resonance", "type": "control"}, "u9": {"operates": {"qubits": [4, 5]}, "purpose": "cross-resonance", "type": "control"}, "u90": {"operates": {"qubits": [40, 41]}, "purpose": "cross-resonance", "type": "control"}, "u91": {"operates": {"qubits": [41, 40]}, "purpose": "cross-resonance", "type": "control"}, "u92": {"operates": {"qubits": [41, 42]}, "purpose": "cross-resonance", "type": "control"}, "u93": {"operates": {"qubits": [41, 53]}, "purpose": "cross-resonance", "type": "control"}, "u94": {"operates": {"qubits": [42, 41]}, "purpose": "cross-resonance", "type": "control"}, "u95": {"operates": {"qubits": [42, 43]}, "purpose": "cross-resonance", "type": "control"}, "u96": {"operates": {"qubits": [43, 34]}, "purpose": "cross-resonance", "type": "control"}, "u97": {"operates": {"qubits": [43, 42]}, "purpose": "cross-resonance", "type": "control"}, "u98": {"operates": {"qubits": [43, 44]}, "purpose": "cross-resonance", "type": "control"}, "u99": {"operates": {"qubits": [44, 43]}, "purpose": "cross-resonance", "type": "control"}}, "clops": null, "clops_h": 250000, "clops_v": "None", "conditional_latency": [], "coords": [[1, 1], [2, 1], [3, 1], [4, 1], [5, 1], [6, 1], [7, 1], [8, 1], [9, 1], [10, 1], [11, 1], [12, 1], [13, 1], [14, 1], [1, 2], [5, 2], [9, 2], [13, 2], [1, 3], [2, 3], [3, 3], [4, 3], [5, 3], [6, 3], [7, 3], [8, 3], [9, 3], [10, 3], [11, 3], [12, 3], [13, 3], [14, 3], [15, 3], [3, 4], [7, 4], [11, 4], [15, 4], [1, 5], [2, 5], [3, 5], [4, 5], [5, 5], [6, 5], [7, 5], [8, 5], [9, 5], [10, 5], [11, 5], [12, 5], [13, 5], [14, 5], [15, 5], [1, 6], [5, 6], [9, 6], [13, 6], [1, 7], [2, 7], [3, 7], [4, 7], [5, 7], [6, 7], [7, 7], [8, 7], [9, 7], [10, 7], [11, 7], [12, 7], [13, 7], [14, 7], [15, 7], [3, 8], [7, 8], [11, 8], [15, 8], [1, 9], [2, 9], [3, 9], [4, 9], [5, 9], [6, 9], [7, 9], [8, 9], [9, 9], [10, 9], [11, 9], [12, 9], [13, 9], [14, 9], [15, 9], [1, 10], [5, 10], [9, 10], [13, 10], [1, 11], [2, 11], [3, 11], [4, 11], [5, 11], [6, 11], [7, 11], [8, 11], [9, 11], [10, 11], [11, 11], [12, 11], [13, 11], [14, 11], [15, 11], [3, 12], [7, 12], [11, 12], [15, 12], [2, 13], [3, 13], [4, 13], [5, 13], [6, 13], [7, 13], [8, 13], [9, 13], [10, 13], [11, 13], [12, 13], [13, 13], [14, 13], [15, 13]], "hamiltonian": {"description": "Qubits are modeled as Duffing oscillators. In this case, the system includes higher energy states, i.e. not just |0> and |1>. The Pauli operators are generalized via the following set of transformations:\n\n$(\\mathbb{I}-\\sigma_{i}^z)/2 \\rightarrow O_i \\equiv b^\\dagger_{i} b_{i}$,\n\n$\\sigma_{+} \\rightarrow b^\\dagger$,\n\n$\\sigma_{-} \\rightarrow b$,\n\n$\\sigma_{i}^X \\rightarrow b^\\dagger_{i} + b_{i}$.\n\nQubits are coupled through resonator buses. The provided Hamiltonian has been projected into the zero excitation subspace of the resonator buses leading to an effective qubit-qubit flip-flop interaction. The qubit resonance frequencies in the Hamiltonian are the cavity dressed frequencies and not exactly what is returned by the backend defaults, which also includes the dressing due to the qubit-qubit interactions.\n\nQuantities are returned in angular frequencies, with units 2*pi*GHz.\n\nWARNING: Currently not all system Hamiltonian information is available to the public, missing values have been replaced with 0.\n", "h_latex": "\\begin{align} \\mathcal{H}/\\hbar = & \\sum_{i=0}^{126}\\left(\\frac{\\omega_{q,i}}{2}(\\mathbb{I}-\\sigma_i^{z})+\\frac{\\Delta_{i}}{2}(O_i^2-O_i)+\\Omega_{d,i}D_i(t)\\sigma_i^{X}\\right) \\\\ & + J_{62,72}(\\sigma_{62}^{+}\\sigma_{72}^{-}+\\sigma_{62}^{-}\\sigma_{72}^{+}) + J_{67,68}(\\sigma_{67}^{+}\\sigma_{68}^{-}+\\sigma_{67}^{-}\\sigma_{68}^{+}) + J_{99,100}(\\sigma_{99}^{+}\\sigma_{100}^{-}+\\sigma_{99}^{-}\\sigma_{100}^{+}) + J_{44,45}(\\sigma_{44}^{+}\\sigma_{45}^{-}+\\sigma_{44}^{-}\\sigma_{45}^{+}) \\\\ & + J_{108,112}(\\sigma_{108}^{+}\\sigma_{112}^{-}+\\sigma_{108}^{-}\\sigma_{112}^{+}) + J_{8,9}(\\sigma_{8}^{+}\\sigma_{9}^{-}+\\sigma_{8}^{-}\\sigma_{9}^{+}) + J_{40,41}(\\sigma_{40}^{+}\\sigma_{41}^{-}+\\sigma_{40}^{-}\\sigma_{41}^{+}) + J_{0,14}(\\sigma_{0}^{+}\\sigma_{14}^{-}+\\sigma_{0}^{-}\\sigma_{14}^{+}) \\\\ & + J_{17,30}(\\sigma_{17}^{+}\\sigma_{30}^{-}+\\sigma_{17}^{-}\\sigma_{30}^{+}) + J_{100,101}(\\sigma_{100}^{+}\\sigma_{101}^{-}+\\sigma_{100}^{-}\\sigma_{101}^{+}) + J_{91,98}(\\sigma_{91}^{+}\\sigma_{98}^{-}+\\sigma_{91}^{-}\\sigma_{98}^{+}) + J_{100,110}(\\sigma_{100}^{+}\\sigma_{110}^{-}+\\sigma_{100}^{-}\\sigma_{110}^{+}) \\\\ & + J_{75,90}(\\sigma_{75}^{+}\\sigma_{90}^{-}+\\sigma_{75}^{-}\\sigma_{90}^{+}) + J_{41,42}(\\sigma_{41}^{+}\\sigma_{42}^{-}+\\sigma_{41}^{-}\\sigma_{42}^{+}) + J_{96,97}(\\sigma_{96}^{+}\\sigma_{97}^{-}+\\sigma_{96}^{-}\\sigma_{97}^{+}) + J_{18,19}(\\sigma_{18}^{+}\\sigma_{19}^{-}+\\sigma_{18}^{-}\\sigma_{19}^{+}) \\\\ & + J_{55,68}(\\sigma_{55}^{+}\\sigma_{68}^{-}+\\sigma_{55}^{-}\\sigma_{68}^{+}) + J_{9,10}(\\sigma_{9}^{+}\\sigma_{10}^{-}+\\sigma_{9}^{-}\\sigma_{10}^{+}) + J_{49,55}(\\sigma_{49}^{+}\\sigma_{55}^{-}+\\sigma_{49}^{-}\\sigma_{55}^{+}) + J_{106,107}(\\sigma_{106}^{+}\\sigma_{107}^{-}+\\sigma_{106}^{-}\\sigma_{107}^{+}) \\\\ & + J_{47,48}(\\sigma_{47}^{+}\\sigma_{48}^{-}+\\sigma_{47}^{-}\\sigma_{48}^{+}) + J_{42,43}(\\sigma_{42}^{+}\\sigma_{43}^{-}+\\sigma_{42}^{-}\\sigma_{43}^{+}) + J_{107,108}(\\sigma_{107}^{+}\\sigma_{108}^{-}+\\sigma_{107}^{-}\\sigma_{108}^{+}) + J_{73,85}(\\sigma_{73}^{+}\\sigma_{85}^{-}+\\sigma_{73}^{-}\\sigma_{85}^{+}) \\\\ & + J_{38,39}(\\sigma_{38}^{+}\\sigma_{39}^{-}+\\sigma_{38}^{-}\\sigma_{39}^{+}) + J_{20,33}(\\sigma_{20}^{+}\\sigma_{33}^{-}+\\sigma_{20}^{-}\\sigma_{33}^{+}) + J_{48,49}(\\sigma_{48}^{+}\\sigma_{49}^{-}+\\sigma_{48}^{-}\\sigma_{49}^{+}) + J_{103,104}(\\sigma_{103}^{+}\\sigma_{104}^{-}+\\sigma_{103}^{-}\\sigma_{104}^{+}) \\\\ & + J_{80,81}(\\sigma_{80}^{+}\\sigma_{81}^{-}+\\sigma_{80}^{-}\\sigma_{81}^{+}) + J_{75,76}(\\sigma_{75}^{+}\\sigma_{76}^{-}+\\sigma_{75}^{-}\\sigma_{76}^{+}) + J_{66,73}(\\sigma_{66}^{+}\\sigma_{73}^{-}+\\sigma_{66}^{-}\\sigma_{73}^{+}) + J_{85,86}(\\sigma_{85}^{+}\\sigma_{86}^{-}+\\sigma_{85}^{-}\\sigma_{86}^{+}) \\\\ & + J_{81,82}(\\sigma_{81}^{+}\\sigma_{82}^{-}+\\sigma_{81}^{-}\\sigma_{82}^{+}) + J_{110,118}(\\sigma_{110}^{+}\\sigma_{118}^{-}+\\sigma_{110}^{-}\\sigma_{118}^{+}) + J_{16,26}(\\sigma_{16}^{+}\\sigma_{26}^{-}+\\sigma_{16}^{-}\\sigma_{26}^{+}) + J_{90,94}(\\sigma_{90}^{+}\\sigma_{94}^{-}+\\sigma_{90}^{-}\\sigma_{94}^{+}) \\\\ & + J_{118,119}(\\sigma_{118}^{+}\\sigma_{119}^{-}+\\sigma_{118}^{-}\\sigma_{119}^{+}) + J_{12,13}(\\sigma_{12}^{+}\\sigma_{13}^{-}+\\sigma_{12}^{-}\\sigma_{13}^{+}) + J_{77,78}(\\sigma_{77}^{+}\\sigma_{78}^{-}+\\sigma_{77}^{-}\\sigma_{78}^{+}) + J_{22,23}(\\sigma_{22}^{+}\\sigma_{23}^{-}+\\sigma_{22}^{-}\\sigma_{23}^{+}) \\\\ & + J_{104,105}(\\sigma_{104}^{+}\\sigma_{105}^{-}+\\sigma_{104}^{-}\\sigma_{105}^{+}) + J_{49,50}(\\sigma_{49}^{+}\\sigma_{50}^{-}+\\sigma_{49}^{-}\\sigma_{50}^{+}) + J_{114,115}(\\sigma_{114}^{+}\\sigma_{115}^{-}+\\sigma_{114}^{-}\\sigma_{115}^{+}) + J_{45,46}(\\sigma_{45}^{+}\\sigma_{46}^{-}+\\sigma_{45}^{-}\\sigma_{46}^{+}) \\\\ & + J_{50,51}(\\sigma_{50}^{+}\\sigma_{51}^{-}+\\sigma_{50}^{-}\\sigma_{51}^{+}) + J_{105,106}(\\sigma_{105}^{+}\\sigma_{106}^{-}+\\sigma_{105}^{-}\\sigma_{106}^{+}) + J_{72,81}(\\sigma_{72}^{+}\\sigma_{81}^{-}+\\sigma_{72}^{-}\\sigma_{81}^{+}) + J_{82,83}(\\sigma_{82}^{+}\\sigma_{83}^{-}+\\sigma_{82}^{-}\\sigma_{83}^{+}) \\\\ & + J_{46,47}(\\sigma_{46}^{+}\\sigma_{47}^{-}+\\sigma_{46}^{-}\\sigma_{47}^{+}) + J_{23,24}(\\sigma_{23}^{+}\\sigma_{24}^{-}+\\sigma_{23}^{-}\\sigma_{24}^{+}) + J_{78,79}(\\sigma_{78}^{+}\\sigma_{79}^{-}+\\sigma_{78}^{-}\\sigma_{79}^{+}) + J_{83,84}(\\sigma_{83}^{+}\\sigma_{84}^{-}+\\sigma_{83}^{-}\\sigma_{84}^{+}) \\\\ & + J_{115,116}(\\sigma_{115}^{+}\\sigma_{116}^{-}+\\sigma_{115}^{-}\\sigma_{116}^{+}) + J_{19,20}(\\sigma_{19}^{+}\\sigma_{20}^{-}+\\sigma_{19}^{-}\\sigma_{20}^{+}) + J_{79,80}(\\sigma_{79}^{+}\\sigma_{80}^{-}+\\sigma_{79}^{-}\\sigma_{80}^{+}) + J_{24,25}(\\sigma_{24}^{+}\\sigma_{25}^{-}+\\sigma_{24}^{-}\\sigma_{25}^{+}) \\\\ & + J_{56,57}(\\sigma_{56}^{+}\\sigma_{57}^{-}+\\sigma_{56}^{-}\\sigma_{57}^{+}) + J_{93,106}(\\sigma_{93}^{+}\\sigma_{106}^{-}+\\sigma_{93}^{-}\\sigma_{106}^{+}) + J_{116,117}(\\sigma_{116}^{+}\\sigma_{117}^{-}+\\sigma_{116}^{-}\\sigma_{117}^{+}) + J_{20,21}(\\sigma_{20}^{+}\\sigma_{21}^{-}+\\sigma_{20}^{-}\\sigma_{21}^{+}) \\\\ & + J_{41,53}(\\sigma_{41}^{+}\\sigma_{53}^{-}+\\sigma_{41}^{-}\\sigma_{53}^{+}) + J_{12,17}(\\sigma_{12}^{+}\\sigma_{17}^{-}+\\sigma_{12}^{-}\\sigma_{17}^{+}) + J_{57,58}(\\sigma_{57}^{+}\\sigma_{58}^{-}+\\sigma_{57}^{-}\\sigma_{58}^{+}) + J_{87,93}(\\sigma_{87}^{+}\\sigma_{93}^{-}+\\sigma_{87}^{-}\\sigma_{93}^{+}) \\\\ & + J_{30,31}(\\sigma_{30}^{+}\\sigma_{31}^{-}+\\sigma_{30}^{-}\\sigma_{31}^{+}) + J_{25,26}(\\sigma_{25}^{+}\\sigma_{26}^{-}+\\sigma_{25}^{-}\\sigma_{26}^{+}) + J_{79,91}(\\sigma_{79}^{+}\\sigma_{91}^{-}+\\sigma_{79}^{-}\\sigma_{91}^{+}) + J_{26,27}(\\sigma_{26}^{+}\\sigma_{27}^{-}+\\sigma_{26}^{-}\\sigma_{27}^{+}) \\\\ & + J_{21,22}(\\sigma_{21}^{+}\\sigma_{22}^{-}+\\sigma_{21}^{-}\\sigma_{22}^{+}) + J_{58,71}(\\sigma_{58}^{+}\\sigma_{71}^{-}+\\sigma_{58}^{-}\\sigma_{71}^{+}) + J_{86,87}(\\sigma_{86}^{+}\\sigma_{87}^{-}+\\sigma_{86}^{-}\\sigma_{87}^{+}) + J_{4,15}(\\sigma_{4}^{+}\\sigma_{15}^{-}+\\sigma_{4}^{-}\\sigma_{15}^{+}) \\\\ & + J_{31,32}(\\sigma_{31}^{+}\\sigma_{32}^{-}+\\sigma_{31}^{-}\\sigma_{32}^{+}) + J_{113,114}(\\sigma_{113}^{+}\\sigma_{114}^{-}+\\sigma_{113}^{-}\\sigma_{114}^{+}) + J_{104,111}(\\sigma_{104}^{+}\\sigma_{111}^{-}+\\sigma_{104}^{-}\\sigma_{111}^{+}) + J_{123,124}(\\sigma_{123}^{+}\\sigma_{124}^{-}+\\sigma_{123}^{-}\\sigma_{124}^{+}) \\\\ & + J_{27,28}(\\sigma_{27}^{+}\\sigma_{28}^{-}+\\sigma_{27}^{-}\\sigma_{28}^{+}) + J_{34,43}(\\sigma_{34}^{+}\\sigma_{43}^{-}+\\sigma_{34}^{-}\\sigma_{43}^{+}) + J_{64,65}(\\sigma_{64}^{+}\\sigma_{65}^{-}+\\sigma_{64}^{-}\\sigma_{65}^{+}) + J_{119,120}(\\sigma_{119}^{+}\\sigma_{120}^{-}+\\sigma_{119}^{-}\\sigma_{120}^{+}) \\\\ & + J_{54,64}(\\sigma_{54}^{+}\\sigma_{64}^{-}+\\sigma_{54}^{-}\\sigma_{64}^{+}) + J_{32,36}(\\sigma_{32}^{+}\\sigma_{36}^{-}+\\sigma_{32}^{-}\\sigma_{36}^{+}) + J_{5,6}(\\sigma_{5}^{+}\\sigma_{6}^{-}+\\sigma_{5}^{-}\\sigma_{6}^{+}) + J_{60,61}(\\sigma_{60}^{+}\\sigma_{61}^{-}+\\sigma_{60}^{-}\\sigma_{61}^{+}) \\\\ & + J_{14,18}(\\sigma_{14}^{+}\\sigma_{18}^{-}+\\sigma_{14}^{-}\\sigma_{18}^{+}) + J_{87,88}(\\sigma_{87}^{+}\\sigma_{88}^{-}+\\sigma_{87}^{-}\\sigma_{88}^{+}) + J_{97,98}(\\sigma_{97}^{+}\\sigma_{98}^{-}+\\sigma_{97}^{-}\\sigma_{98}^{+}) + J_{1,2}(\\sigma_{1}^{+}\\sigma_{2}^{-}+\\sigma_{1}^{-}\\sigma_{2}^{+}) \\\\ & + J_{112,126}(\\sigma_{112}^{+}\\sigma_{126}^{-}+\\sigma_{112}^{-}\\sigma_{126}^{+}) + J_{28,29}(\\sigma_{28}^{+}\\sigma_{29}^{-}+\\sigma_{28}^{-}\\sigma_{29}^{+}) + J_{45,54}(\\sigma_{45}^{+}\\sigma_{54}^{-}+\\sigma_{45}^{-}\\sigma_{54}^{+}) + J_{36,51}(\\sigma_{36}^{+}\\sigma_{51}^{-}+\\sigma_{36}^{-}\\sigma_{51}^{+}) \\\\ & + J_{88,89}(\\sigma_{88}^{+}\\sigma_{89}^{-}+\\sigma_{88}^{-}\\sigma_{89}^{+}) + J_{120,121}(\\sigma_{120}^{+}\\sigma_{121}^{-}+\\sigma_{120}^{-}\\sigma_{121}^{+}) + J_{15,22}(\\sigma_{15}^{+}\\sigma_{22}^{-}+\\sigma_{15}^{-}\\sigma_{22}^{+}) + J_{24,34}(\\sigma_{24}^{+}\\sigma_{34}^{-}+\\sigma_{24}^{-}\\sigma_{34}^{+}) \\\\ & + J_{84,85}(\\sigma_{84}^{+}\\sigma_{85}^{-}+\\sigma_{84}^{-}\\sigma_{85}^{+}) + J_{29,30}(\\sigma_{29}^{+}\\sigma_{30}^{-}+\\sigma_{29}^{-}\\sigma_{30}^{+}) + J_{61,62}(\\sigma_{61}^{+}\\sigma_{62}^{-}+\\sigma_{61}^{-}\\sigma_{62}^{+}) + J_{70,74}(\\sigma_{70}^{+}\\sigma_{74}^{-}+\\sigma_{70}^{-}\\sigma_{74}^{+}) \\\\ & + J_{121,122}(\\sigma_{121}^{+}\\sigma_{122}^{-}+\\sigma_{121}^{-}\\sigma_{122}^{+}) + J_{2,3}(\\sigma_{2}^{+}\\sigma_{3}^{-}+\\sigma_{2}^{-}\\sigma_{3}^{+}) + J_{122,123}(\\sigma_{122}^{+}\\sigma_{123}^{-}+\\sigma_{122}^{-}\\sigma_{123}^{+}) + J_{117,118}(\\sigma_{117}^{+}\\sigma_{118}^{-}+\\sigma_{117}^{-}\\sigma_{118}^{+}) \\\\ & + J_{62,63}(\\sigma_{62}^{+}\\sigma_{63}^{-}+\\sigma_{62}^{-}\\sigma_{63}^{+}) + J_{109,114}(\\sigma_{109}^{+}\\sigma_{114}^{-}+\\sigma_{109}^{-}\\sigma_{114}^{+}) + J_{94,95}(\\sigma_{94}^{+}\\sigma_{95}^{-}+\\sigma_{94}^{-}\\sigma_{95}^{+}) + J_{37,52}(\\sigma_{37}^{+}\\sigma_{52}^{-}+\\sigma_{37}^{-}\\sigma_{52}^{+}) \\\\ & + J_{58,59}(\\sigma_{58}^{+}\\sigma_{59}^{-}+\\sigma_{58}^{-}\\sigma_{59}^{+}) + J_{3,4}(\\sigma_{3}^{+}\\sigma_{4}^{-}+\\sigma_{3}^{-}\\sigma_{4}^{+}) + J_{33,39}(\\sigma_{33}^{+}\\sigma_{39}^{-}+\\sigma_{33}^{-}\\sigma_{39}^{+}) + J_{95,96}(\\sigma_{95}^{+}\\sigma_{96}^{-}+\\sigma_{95}^{-}\\sigma_{96}^{+}) \\\\ & + J_{68,69}(\\sigma_{68}^{+}\\sigma_{69}^{-}+\\sigma_{68}^{-}\\sigma_{69}^{+}) + J_{63,64}(\\sigma_{63}^{+}\\sigma_{64}^{-}+\\sigma_{63}^{-}\\sigma_{64}^{+}) + J_{71,77}(\\sigma_{71}^{+}\\sigma_{77}^{-}+\\sigma_{71}^{-}\\sigma_{77}^{+}) + J_{111,122}(\\sigma_{111}^{+}\\sigma_{122}^{-}+\\sigma_{111}^{-}\\sigma_{122}^{+}) \\\\ & + J_{4,5}(\\sigma_{4}^{+}\\sigma_{5}^{-}+\\sigma_{4}^{-}\\sigma_{5}^{+}) + J_{59,60}(\\sigma_{59}^{+}\\sigma_{60}^{-}+\\sigma_{59}^{-}\\sigma_{60}^{+}) + J_{96,109}(\\sigma_{96}^{+}\\sigma_{109}^{-}+\\sigma_{96}^{-}\\sigma_{109}^{+}) + J_{124,125}(\\sigma_{124}^{+}\\sigma_{125}^{-}+\\sigma_{124}^{-}\\sigma_{125}^{+}) \\\\ & + J_{69,70}(\\sigma_{69}^{+}\\sigma_{70}^{-}+\\sigma_{69}^{-}\\sigma_{70}^{+}) + J_{35,47}(\\sigma_{35}^{+}\\sigma_{47}^{-}+\\sigma_{35}^{-}\\sigma_{47}^{+}) + J_{101,102}(\\sigma_{101}^{+}\\sigma_{102}^{-}+\\sigma_{101}^{-}\\sigma_{102}^{+}) + J_{0,1}(\\sigma_{0}^{+}\\sigma_{1}^{-}+\\sigma_{0}^{-}\\sigma_{1}^{+}) \\\\ & + J_{10,11}(\\sigma_{10}^{+}\\sigma_{11}^{-}+\\sigma_{10}^{-}\\sigma_{11}^{+}) + J_{65,66}(\\sigma_{65}^{+}\\sigma_{66}^{-}+\\sigma_{65}^{-}\\sigma_{66}^{+}) + J_{37,38}(\\sigma_{37}^{+}\\sigma_{38}^{-}+\\sigma_{37}^{-}\\sigma_{38}^{+}) + J_{28,35}(\\sigma_{28}^{+}\\sigma_{35}^{-}+\\sigma_{28}^{-}\\sigma_{35}^{+}) \\\\ & + J_{102,103}(\\sigma_{102}^{+}\\sigma_{103}^{-}+\\sigma_{102}^{-}\\sigma_{103}^{+}) + J_{92,102}(\\sigma_{92}^{+}\\sigma_{102}^{-}+\\sigma_{92}^{-}\\sigma_{102}^{+}) + J_{6,7}(\\sigma_{6}^{+}\\sigma_{7}^{-}+\\sigma_{6}^{-}\\sigma_{7}^{+}) + J_{98,99}(\\sigma_{98}^{+}\\sigma_{99}^{-}+\\sigma_{98}^{-}\\sigma_{99}^{+}) \\\\ & + J_{43,44}(\\sigma_{43}^{+}\\sigma_{44}^{-}+\\sigma_{43}^{-}\\sigma_{44}^{+}) + J_{52,56}(\\sigma_{52}^{+}\\sigma_{56}^{-}+\\sigma_{52}^{-}\\sigma_{56}^{+}) + J_{125,126}(\\sigma_{125}^{+}\\sigma_{126}^{-}+\\sigma_{125}^{-}\\sigma_{126}^{+}) + J_{39,40}(\\sigma_{39}^{+}\\sigma_{40}^{-}+\\sigma_{39}^{-}\\sigma_{40}^{+}) \\\\ & + J_{8,16}(\\sigma_{8}^{+}\\sigma_{16}^{-}+\\sigma_{8}^{-}\\sigma_{16}^{+}) + J_{66,67}(\\sigma_{66}^{+}\\sigma_{67}^{-}+\\sigma_{66}^{-}\\sigma_{67}^{+}) + J_{11,12}(\\sigma_{11}^{+}\\sigma_{12}^{-}+\\sigma_{11}^{-}\\sigma_{12}^{+}) + J_{76,77}(\\sigma_{76}^{+}\\sigma_{77}^{-}+\\sigma_{76}^{-}\\sigma_{77}^{+}) \\\\ & + J_{83,92}(\\sigma_{83}^{+}\\sigma_{92}^{-}+\\sigma_{83}^{-}\\sigma_{92}^{+}) + J_{74,89}(\\sigma_{74}^{+}\\sigma_{89}^{-}+\\sigma_{74}^{-}\\sigma_{89}^{+}) + J_{7,8}(\\sigma_{7}^{+}\\sigma_{8}^{-}+\\sigma_{7}^{-}\\sigma_{8}^{+}) + J_{53,60}(\\sigma_{53}^{+}\\sigma_{60}^{-}+\\sigma_{53}^{-}\\sigma_{60}^{+}) \\\\ & + \\Omega_{d,0}(U_{0}^{(0,1)}(t)+U_{1}^{(0,14)}(t))\\sigma_{0}^{X} + \\Omega_{d,1}(U_{3}^{(1,2)}(t)+U_{2}^{(1,0)}(t))\\sigma_{1}^{X} \\\\ & + \\Omega_{d,2}(U_{5}^{(2,3)}(t)+U_{4}^{(2,1)}(t))\\sigma_{2}^{X} + \\Omega_{d,3}(U_{7}^{(3,4)}(t)+U_{6}^{(3,2)}(t))\\sigma_{3}^{X} \\\\ & + \\Omega_{d,4}(U_{10}^{(4,15)}(t)+U_{9}^{(4,5)}(t)+U_{8}^{(4,3)}(t))\\sigma_{4}^{X} + \\Omega_{d,5}(U_{12}^{(5,6)}(t)+U_{11}^{(5,4)}(t))\\sigma_{5}^{X} \\\\ & + \\Omega_{d,6}(U_{14}^{(6,7)}(t)+U_{13}^{(6,5)}(t))\\sigma_{6}^{X} + \\Omega_{d,7}(U_{16}^{(7,8)}(t)+U_{15}^{(7,6)}(t))\\sigma_{7}^{X} \\\\ & + \\Omega_{d,8}(U_{18}^{(8,9)}(t)+U_{17}^{(8,7)}(t)+U_{19}^{(8,16)}(t))\\sigma_{8}^{X} + \\Omega_{d,9}(U_{21}^{(9,10)}(t)+U_{20}^{(9,8)}(t))\\sigma_{9}^{X} \\\\ & + \\Omega_{d,10}(U_{23}^{(10,11)}(t)+U_{22}^{(10,9)}(t))\\sigma_{10}^{X} + \\Omega_{d,11}(U_{25}^{(11,12)}(t)+U_{24}^{(11,10)}(t))\\sigma_{11}^{X} \\\\ & + \\Omega_{d,12}(U_{27}^{(12,13)}(t)+U_{28}^{(12,17)}(t)+U_{26}^{(12,11)}(t))\\sigma_{12}^{X} + \\Omega_{d,13}(U_{29}^{(13,12)}(t))\\sigma_{13}^{X} \\\\ & + \\Omega_{d,14}(U_{31}^{(14,18)}(t)+U_{30}^{(14,0)}(t))\\sigma_{14}^{X} + \\Omega_{d,15}(U_{32}^{(15,4)}(t)+U_{33}^{(15,22)}(t))\\sigma_{15}^{X} \\\\ & + \\Omega_{d,16}(U_{35}^{(16,26)}(t)+U_{34}^{(16,8)}(t))\\sigma_{16}^{X} + \\Omega_{d,17}(U_{36}^{(17,12)}(t)+U_{37}^{(17,30)}(t))\\sigma_{17}^{X} \\\\ & + \\Omega_{d,18}(U_{39}^{(18,19)}(t)+U_{38}^{(18,14)}(t))\\sigma_{18}^{X} + \\Omega_{d,19}(U_{41}^{(19,20)}(t)+U_{40}^{(19,18)}(t))\\sigma_{19}^{X} \\\\ & + \\Omega_{d,20}(U_{43}^{(20,21)}(t)+U_{42}^{(20,19)}(t)+U_{44}^{(20,33)}(t))\\sigma_{20}^{X} + \\Omega_{d,21}(U_{46}^{(21,22)}(t)+U_{45}^{(21,20)}(t))\\sigma_{21}^{X} \\\\ & + \\Omega_{d,22}(U_{49}^{(22,23)}(t)+U_{48}^{(22,21)}(t)+U_{47}^{(22,15)}(t))\\sigma_{22}^{X} + \\Omega_{d,23}(U_{50}^{(23,22)}(t)+U_{51}^{(23,24)}(t))\\sigma_{23}^{X} \\\\ & + \\Omega_{d,24}(U_{52}^{(24,23)}(t)+U_{54}^{(24,34)}(t)+U_{53}^{(24,25)}(t))\\sigma_{24}^{X} + \\Omega_{d,25}(U_{56}^{(25,26)}(t)+U_{55}^{(25,24)}(t))\\sigma_{25}^{X} \\\\ & + \\Omega_{d,26}(U_{58}^{(26,25)}(t)+U_{59}^{(26,27)}(t)+U_{57}^{(26,16)}(t))\\sigma_{26}^{X} + \\Omega_{d,27}(U_{61}^{(27,28)}(t)+U_{60}^{(27,26)}(t))\\sigma_{27}^{X} \\\\ & + \\Omega_{d,28}(U_{63}^{(28,29)}(t)+U_{62}^{(28,27)}(t)+U_{64}^{(28,35)}(t))\\sigma_{28}^{X} + \\Omega_{d,29}(U_{66}^{(29,30)}(t)+U_{65}^{(29,28)}(t))\\sigma_{29}^{X} \\\\ & + \\Omega_{d,30}(U_{67}^{(30,17)}(t)+U_{69}^{(30,31)}(t)+U_{68}^{(30,29)}(t))\\sigma_{30}^{X} + \\Omega_{d,31}(U_{70}^{(31,30)}(t)+U_{71}^{(31,32)}(t))\\sigma_{31}^{X} \\\\ & + \\Omega_{d,32}(U_{73}^{(32,36)}(t)+U_{72}^{(32,31)}(t))\\sigma_{32}^{X} + \\Omega_{d,33}(U_{75}^{(33,39)}(t)+U_{74}^{(33,20)}(t))\\sigma_{33}^{X} \\\\ & + \\Omega_{d,34}(U_{77}^{(34,43)}(t)+U_{76}^{(34,24)}(t))\\sigma_{34}^{X} + \\Omega_{d,35}(U_{79}^{(35,47)}(t)+U_{78}^{(35,28)}(t))\\sigma_{35}^{X} \\\\ & + \\Omega_{d,36}(U_{81}^{(36,51)}(t)+U_{80}^{(36,32)}(t))\\sigma_{36}^{X} + \\Omega_{d,37}(U_{83}^{(37,52)}(t)+U_{82}^{(37,38)}(t))\\sigma_{37}^{X} \\\\ & + \\Omega_{d,38}(U_{85}^{(38,39)}(t)+U_{84}^{(38,37)}(t))\\sigma_{38}^{X} + \\Omega_{d,39}(U_{86}^{(39,33)}(t)+U_{88}^{(39,40)}(t)+U_{87}^{(39,38)}(t))\\sigma_{39}^{X} \\\\ & + \\Omega_{d,40}(U_{90}^{(40,41)}(t)+U_{89}^{(40,39)}(t))\\sigma_{40}^{X} + \\Omega_{d,41}(U_{93}^{(41,53)}(t)+U_{92}^{(41,42)}(t)+U_{91}^{(41,40)}(t))\\sigma_{41}^{X} \\\\ & + \\Omega_{d,42}(U_{95}^{(42,43)}(t)+U_{94}^{(42,41)}(t))\\sigma_{42}^{X} + \\Omega_{d,43}(U_{96}^{(43,34)}(t)+U_{98}^{(43,44)}(t)+U_{97}^{(43,42)}(t))\\sigma_{43}^{X} \\\\ & + \\Omega_{d,44}(U_{100}^{(44,45)}(t)+U_{99}^{(44,43)}(t))\\sigma_{44}^{X} + \\Omega_{d,45}(U_{103}^{(45,54)}(t)+U_{102}^{(45,46)}(t)+U_{101}^{(45,44)}(t))\\sigma_{45}^{X} \\\\ & + \\Omega_{d,46}(U_{104}^{(46,45)}(t)+U_{105}^{(46,47)}(t))\\sigma_{46}^{X} + \\Omega_{d,47}(U_{106}^{(47,35)}(t)+U_{108}^{(47,48)}(t)+U_{107}^{(47,46)}(t))\\sigma_{47}^{X} \\\\ & + \\Omega_{d,48}(U_{109}^{(48,47)}(t)+U_{110}^{(48,49)}(t))\\sigma_{48}^{X} + \\Omega_{d,49}(U_{113}^{(49,55)}(t)+U_{111}^{(49,48)}(t)+U_{112}^{(49,50)}(t))\\sigma_{49}^{X} \\\\ & + \\Omega_{d,50}(U_{115}^{(50,51)}(t)+U_{114}^{(50,49)}(t))\\sigma_{50}^{X} + \\Omega_{d,51}(U_{117}^{(51,50)}(t)+U_{116}^{(51,36)}(t))\\sigma_{51}^{X} \\\\ & + \\Omega_{d,52}(U_{119}^{(52,56)}(t)+U_{118}^{(52,37)}(t))\\sigma_{52}^{X} + \\Omega_{d,53}(U_{121}^{(53,60)}(t)+U_{120}^{(53,41)}(t))\\sigma_{53}^{X} \\\\ & + \\Omega_{d,54}(U_{123}^{(54,64)}(t)+U_{122}^{(54,45)}(t))\\sigma_{54}^{X} + \\Omega_{d,55}(U_{125}^{(55,68)}(t)+U_{124}^{(55,49)}(t))\\sigma_{55}^{X} \\\\ & + \\Omega_{d,56}(U_{126}^{(56,52)}(t)+U_{127}^{(56,57)}(t))\\sigma_{56}^{X} + \\Omega_{d,57}(U_{129}^{(57,58)}(t)+U_{128}^{(57,56)}(t))\\sigma_{57}^{X} \\\\ & + \\Omega_{d,58}(U_{132}^{(58,71)}(t)+U_{131}^{(58,59)}(t)+U_{130}^{(58,57)}(t))\\sigma_{58}^{X} + \\Omega_{d,59}(U_{133}^{(59,58)}(t)+U_{134}^{(59,60)}(t))\\sigma_{59}^{X} \\\\ & + \\Omega_{d,60}(U_{137}^{(60,61)}(t)+U_{136}^{(60,59)}(t)+U_{135}^{(60,53)}(t))\\sigma_{60}^{X} + \\Omega_{d,61}(U_{139}^{(61,62)}(t)+U_{138}^{(61,60)}(t))\\sigma_{61}^{X} \\\\ & + \\Omega_{d,62}(U_{142}^{(62,72)}(t)+U_{140}^{(62,61)}(t)+U_{141}^{(62,63)}(t))\\sigma_{62}^{X} + \\Omega_{d,63}(U_{144}^{(63,64)}(t)+U_{143}^{(63,62)}(t))\\sigma_{63}^{X} \\\\ & + \\Omega_{d,64}(U_{147}^{(64,65)}(t)+U_{145}^{(64,54)}(t)+U_{146}^{(64,63)}(t))\\sigma_{64}^{X} + \\Omega_{d,65}(U_{149}^{(65,66)}(t)+U_{148}^{(65,64)}(t))\\sigma_{65}^{X} \\\\ & + \\Omega_{d,66}(U_{151}^{(66,67)}(t)+U_{152}^{(66,73)}(t)+U_{150}^{(66,65)}(t))\\sigma_{66}^{X} + \\Omega_{d,67}(U_{154}^{(67,68)}(t)+U_{153}^{(67,66)}(t))\\sigma_{67}^{X} \\\\ & + \\Omega_{d,68}(U_{156}^{(68,67)}(t)+U_{155}^{(68,55)}(t)+U_{157}^{(68,69)}(t))\\sigma_{68}^{X} + \\Omega_{d,69}(U_{158}^{(69,68)}(t)+U_{159}^{(69,70)}(t))\\sigma_{69}^{X} \\\\ & + \\Omega_{d,70}(U_{160}^{(70,69)}(t)+U_{161}^{(70,74)}(t))\\sigma_{70}^{X} + \\Omega_{d,71}(U_{163}^{(71,77)}(t)+U_{162}^{(71,58)}(t))\\sigma_{71}^{X} \\\\ & + \\Omega_{d,72}(U_{165}^{(72,81)}(t)+U_{164}^{(72,62)}(t))\\sigma_{72}^{X} + \\Omega_{d,73}(U_{167}^{(73,85)}(t)+U_{166}^{(73,66)}(t))\\sigma_{73}^{X} \\\\ & + \\Omega_{d,74}(U_{168}^{(74,70)}(t)+U_{169}^{(74,89)}(t))\\sigma_{74}^{X} + \\Omega_{d,75}(U_{170}^{(75,76)}(t)+U_{171}^{(75,90)}(t))\\sigma_{75}^{X} \\\\ & + \\Omega_{d,76}(U_{173}^{(76,77)}(t)+U_{172}^{(76,75)}(t))\\sigma_{76}^{X} + \\Omega_{d,77}(U_{176}^{(77,78)}(t)+U_{174}^{(77,71)}(t)+U_{175}^{(77,76)}(t))\\sigma_{77}^{X} \\\\ & + \\Omega_{d,78}(U_{178}^{(78,79)}(t)+U_{177}^{(78,77)}(t))\\sigma_{78}^{X} + \\Omega_{d,79}(U_{180}^{(79,80)}(t)+U_{181}^{(79,91)}(t)+U_{179}^{(79,78)}(t))\\sigma_{79}^{X} \\\\ & + \\Omega_{d,80}(U_{183}^{(80,81)}(t)+U_{182}^{(80,79)}(t))\\sigma_{80}^{X} + \\Omega_{d,81}(U_{185}^{(81,80)}(t)+U_{184}^{(81,72)}(t)+U_{186}^{(81,82)}(t))\\sigma_{81}^{X} \\\\ & + \\Omega_{d,82}(U_{187}^{(82,81)}(t)+U_{188}^{(82,83)}(t))\\sigma_{82}^{X} + \\Omega_{d,83}(U_{191}^{(83,92)}(t)+U_{190}^{(83,84)}(t)+U_{189}^{(83,82)}(t))\\sigma_{83}^{X} \\\\ & + \\Omega_{d,84}(U_{192}^{(84,83)}(t)+U_{193}^{(84,85)}(t))\\sigma_{84}^{X} + \\Omega_{d,85}(U_{194}^{(85,73)}(t)+U_{196}^{(85,86)}(t)+U_{195}^{(85,84)}(t))\\sigma_{85}^{X} \\\\ & + \\Omega_{d,86}(U_{198}^{(86,87)}(t)+U_{197}^{(86,85)}(t))\\sigma_{86}^{X} + \\Omega_{d,87}(U_{200}^{(87,88)}(t)+U_{199}^{(87,86)}(t)+U_{201}^{(87,93)}(t))\\sigma_{87}^{X} \\\\ & + \\Omega_{d,88}(U_{203}^{(88,89)}(t)+U_{202}^{(88,87)}(t))\\sigma_{88}^{X} + \\Omega_{d,89}(U_{204}^{(89,74)}(t)+U_{205}^{(89,88)}(t))\\sigma_{89}^{X} \\\\ & + \\Omega_{d,90}(U_{207}^{(90,94)}(t)+U_{206}^{(90,75)}(t))\\sigma_{90}^{X} + \\Omega_{d,91}(U_{209}^{(91,98)}(t)+U_{208}^{(91,79)}(t))\\sigma_{91}^{X} \\\\ & + \\Omega_{d,92}(U_{211}^{(92,102)}(t)+U_{210}^{(92,83)}(t))\\sigma_{92}^{X} + \\Omega_{d,93}(U_{213}^{(93,106)}(t)+U_{212}^{(93,87)}(t))\\sigma_{93}^{X} \\\\ & + \\Omega_{d,94}(U_{214}^{(94,90)}(t)+U_{215}^{(94,95)}(t))\\sigma_{94}^{X} + \\Omega_{d,95}(U_{216}^{(95,94)}(t)+U_{217}^{(95,96)}(t))\\sigma_{95}^{X} \\\\ & + \\Omega_{d,96}(U_{220}^{(96,109)}(t)+U_{219}^{(96,97)}(t)+U_{218}^{(96,95)}(t))\\sigma_{96}^{X} + \\Omega_{d,97}(U_{221}^{(97,96)}(t)+U_{222}^{(97,98)}(t))\\sigma_{97}^{X} \\\\ & + \\Omega_{d,98}(U_{223}^{(98,91)}(t)+U_{225}^{(98,99)}(t)+U_{224}^{(98,97)}(t))\\sigma_{98}^{X} + \\Omega_{d,99}(U_{227}^{(99,100)}(t)+U_{226}^{(99,98)}(t))\\sigma_{99}^{X} \\\\ & + \\Omega_{d,100}(U_{229}^{(100,101)}(t)+U_{228}^{(100,99)}(t)+U_{230}^{(100,110)}(t))\\sigma_{100}^{X} + \\Omega_{d,101}(U_{232}^{(101,102)}(t)+U_{231}^{(101,100)}(t))\\sigma_{101}^{X} \\\\ & + \\Omega_{d,102}(U_{233}^{(102,92)}(t)+U_{234}^{(102,101)}(t)+U_{235}^{(102,103)}(t))\\sigma_{102}^{X} + \\Omega_{d,103}(U_{237}^{(103,104)}(t)+U_{236}^{(103,102)}(t))\\sigma_{103}^{X} \\\\ & + \\Omega_{d,104}(U_{239}^{(104,105)}(t)+U_{238}^{(104,103)}(t)+U_{240}^{(104,111)}(t))\\sigma_{104}^{X} + \\Omega_{d,105}(U_{241}^{(105,104)}(t)+U_{242}^{(105,106)}(t))\\sigma_{105}^{X} \\\\ & + \\Omega_{d,106}(U_{245}^{(106,107)}(t)+U_{244}^{(106,105)}(t)+U_{243}^{(106,93)}(t))\\sigma_{106}^{X} + \\Omega_{d,107}(U_{247}^{(107,108)}(t)+U_{246}^{(107,106)}(t))\\sigma_{107}^{X} \\\\ & + \\Omega_{d,108}(U_{248}^{(108,107)}(t)+U_{249}^{(108,112)}(t))\\sigma_{108}^{X} + \\Omega_{d,109}(U_{250}^{(109,96)}(t)+U_{251}^{(109,114)}(t))\\sigma_{109}^{X} \\\\ & + \\Omega_{d,110}(U_{253}^{(110,118)}(t)+U_{252}^{(110,100)}(t))\\sigma_{110}^{X} + \\Omega_{d,111}(U_{255}^{(111,122)}(t)+U_{254}^{(111,104)}(t))\\sigma_{111}^{X} \\\\ & + \\Omega_{d,112}(U_{256}^{(112,108)}(t)+U_{257}^{(112,126)}(t))\\sigma_{112}^{X} + \\Omega_{d,113}(U_{258}^{(113,114)}(t))\\sigma_{113}^{X} \\\\ & + \\Omega_{d,114}(U_{261}^{(114,115)}(t)+U_{260}^{(114,113)}(t)+U_{259}^{(114,109)}(t))\\sigma_{114}^{X} + \\Omega_{d,115}(U_{263}^{(115,116)}(t)+U_{262}^{(115,114)}(t))\\sigma_{115}^{X} \\\\ & + \\Omega_{d,116}(U_{265}^{(116,117)}(t)+U_{264}^{(116,115)}(t))\\sigma_{116}^{X} + \\Omega_{d,117}(U_{267}^{(117,118)}(t)+U_{266}^{(117,116)}(t))\\sigma_{117}^{X} \\\\ & + \\Omega_{d,118}(U_{270}^{(118,119)}(t)+U_{269}^{(118,117)}(t)+U_{268}^{(118,110)}(t))\\sigma_{118}^{X} + \\Omega_{d,119}(U_{272}^{(119,120)}(t)+U_{271}^{(119,118)}(t))\\sigma_{119}^{X} \\\\ & + \\Omega_{d,120}(U_{274}^{(120,121)}(t)+U_{273}^{(120,119)}(t))\\sigma_{120}^{X} + \\Omega_{d,121}(U_{276}^{(121,122)}(t)+U_{275}^{(121,120)}(t))\\sigma_{121}^{X} \\\\ & + \\Omega_{d,122}(U_{279}^{(122,123)}(t)+U_{277}^{(122,111)}(t)+U_{278}^{(122,121)}(t))\\sigma_{122}^{X} + \\Omega_{d,123}(U_{281}^{(123,124)}(t)+U_{280}^{(123,122)}(t))\\sigma_{123}^{X} \\\\ & + \\Omega_{d,124}(U_{283}^{(124,125)}(t)+U_{282}^{(124,123)}(t))\\sigma_{124}^{X} + \\Omega_{d,125}(U_{285}^{(125,126)}(t)+U_{284}^{(125,124)}(t))\\sigma_{125}^{X} \\\\ & + \\Omega_{d,126}(U_{286}^{(126,112)}(t)+U_{287}^{(126,125)}(t))\\sigma_{126}^{X} \\\\ \\end{align}", "h_str": ["_SUM[i,0,126,wq{i}/2*(I{i}-Z{i})]", "_SUM[i,0,126,delta{i}/2*O{i}*O{i}]", "_SUM[i,0,126,-delta{i}/2*O{i}]", "_SUM[i,0,126,omegad{i}*X{i}||D{i}]", "jq62q72*Sp62*Sm72", "jq62q72*Sm62*Sp72", "jq67q68*Sp67*Sm68", "jq67q68*Sm67*Sp68", "jq99q100*Sp99*Sm100", "jq99q100*Sm99*Sp100", "jq44q45*Sp44*Sm45", "jq44q45*Sm44*Sp45", "jq108q112*Sp108*Sm112", "jq108q112*Sm108*Sp112", "jq8q9*Sp8*Sm9", "jq8q9*Sm8*Sp9", "jq40q41*Sp40*Sm41", "jq40q41*Sm40*Sp41", "jq0q14*Sp0*Sm14", "jq0q14*Sm0*Sp14", "jq17q30*Sp17*Sm30", "jq17q30*Sm17*Sp30", "jq100q101*Sp100*Sm101", "jq100q101*Sm100*Sp101", "jq91q98*Sp91*Sm98", "jq91q98*Sm91*Sp98", "jq100q110*Sp100*Sm110", "jq100q110*Sm100*Sp110", "jq75q90*Sp75*Sm90", "jq75q90*Sm75*Sp90", "jq41q42*Sp41*Sm42", "jq41q42*Sm41*Sp42", "jq96q97*Sp96*Sm97", "jq96q97*Sm96*Sp97", "jq18q19*Sp18*Sm19", "jq18q19*Sm18*Sp19", "jq55q68*Sp55*Sm68", "jq55q68*Sm55*Sp68", "jq9q10*Sp9*Sm10", "jq9q10*Sm9*Sp10", "jq49q55*Sp49*Sm55", "jq49q55*Sm49*Sp55", "jq106q107*Sp106*Sm107", "jq106q107*Sm106*Sp107", "jq47q48*Sp47*Sm48", "jq47q48*Sm47*Sp48", "jq42q43*Sp42*Sm43", "jq42q43*Sm42*Sp43", "jq107q108*Sp107*Sm108", "jq107q108*Sm107*Sp108", "jq73q85*Sp73*Sm85", "jq73q85*Sm73*Sp85", "jq38q39*Sp38*Sm39", "jq38q39*Sm38*Sp39", "jq20q33*Sp20*Sm33", "jq20q33*Sm20*Sp33", "jq48q49*Sp48*Sm49", "jq48q49*Sm48*Sp49", "jq103q104*Sp103*Sm104", "jq103q104*Sm103*Sp104", "jq80q81*Sp80*Sm81", "jq80q81*Sm80*Sp81", "jq75q76*Sp75*Sm76", "jq75q76*Sm75*Sp76", "jq66q73*Sp66*Sm73", "jq66q73*Sm66*Sp73", "jq85q86*Sp85*Sm86", "jq85q86*Sm85*Sp86", "jq81q82*Sp81*Sm82", "jq81q82*Sm81*Sp82", "jq110q118*Sp110*Sm118", "jq110q118*Sm110*Sp118", "jq16q26*Sp16*Sm26", "jq16q26*Sm16*Sp26", "jq90q94*Sp90*Sm94", "jq90q94*Sm90*Sp94", "jq118q119*Sp118*Sm119", "jq118q119*Sm118*Sp119", "jq12q13*Sp12*Sm13", "jq12q13*Sm12*Sp13", "jq77q78*Sp77*Sm78", "jq77q78*Sm77*Sp78", "jq22q23*Sp22*Sm23", "jq22q23*Sm22*Sp23", "jq104q105*Sp104*Sm105", "jq104q105*Sm104*Sp105", "jq49q50*Sp49*Sm50", "jq49q50*Sm49*Sp50", "jq114q115*Sp114*Sm115", "jq114q115*Sm114*Sp115", "jq45q46*Sp45*Sm46", "jq45q46*Sm45*Sp46", "jq50q51*Sp50*Sm51", "jq50q51*Sm50*Sp51", "jq105q106*Sp105*Sm106", "jq105q106*Sm105*Sp106", "jq72q81*Sp72*Sm81", "jq72q81*Sm72*Sp81", "jq82q83*Sp82*Sm83", "jq82q83*Sm82*Sp83", "jq46q47*Sp46*Sm47", "jq46q47*Sm46*Sp47", "jq23q24*Sp23*Sm24", "jq23q24*Sm23*Sp24", "jq78q79*Sp78*Sm79", "jq78q79*Sm78*Sp79", "jq83q84*Sp83*Sm84", "jq83q84*Sm83*Sp84", "jq115q116*Sp115*Sm116", "jq115q116*Sm115*Sp116", "jq19q20*Sp19*Sm20", "jq19q20*Sm19*Sp20", "jq79q80*Sp79*Sm80", "jq79q80*Sm79*Sp80", "jq24q25*Sp24*Sm25", "jq24q25*Sm24*Sp25", "jq56q57*Sp56*Sm57", "jq56q57*Sm56*Sp57", "jq93q106*Sp93*Sm106", "jq93q106*Sm93*Sp106", "jq116q117*Sp116*Sm117", "jq116q117*Sm116*Sp117", "jq20q21*Sp20*Sm21", "jq20q21*Sm20*Sp21", "jq41q53*Sp41*Sm53", "jq41q53*Sm41*Sp53", "jq12q17*Sp12*Sm17", "jq12q17*Sm12*Sp17", "jq57q58*Sp57*Sm58", "jq57q58*Sm57*Sp58", "jq87q93*Sp87*Sm93", "jq87q93*Sm87*Sp93", "jq30q31*Sp30*Sm31", "jq30q31*Sm30*Sp31", "jq25q26*Sp25*Sm26", "jq25q26*Sm25*Sp26", "jq79q91*Sp79*Sm91", "jq79q91*Sm79*Sp91", "jq26q27*Sp26*Sm27", "jq26q27*Sm26*Sp27", "jq21q22*Sp21*Sm22", "jq21q22*Sm21*Sp22", "jq58q71*Sp58*Sm71", "jq58q71*Sm58*Sp71", "jq86q87*Sp86*Sm87", "jq86q87*Sm86*Sp87", "jq4q15*Sp4*Sm15", "jq4q15*Sm4*Sp15", "jq31q32*Sp31*Sm32", "jq31q32*Sm31*Sp32", "jq113q114*Sp113*Sm114", "jq113q114*Sm113*Sp114", "jq104q111*Sp104*Sm111", "jq104q111*Sm104*Sp111", "jq123q124*Sp123*Sm124", "jq123q124*Sm123*Sp124", "jq27q28*Sp27*Sm28", "jq27q28*Sm27*Sp28", "jq34q43*Sp34*Sm43", "jq34q43*Sm34*Sp43", "jq64q65*Sp64*Sm65", "jq64q65*Sm64*Sp65", "jq119q120*Sp119*Sm120", "jq119q120*Sm119*Sp120", "jq54q64*Sp54*Sm64", "jq54q64*Sm54*Sp64", "jq32q36*Sp32*Sm36", "jq32q36*Sm32*Sp36", "jq5q6*Sp5*Sm6", "jq5q6*Sm5*Sp6", "jq60q61*Sp60*Sm61", "jq60q61*Sm60*Sp61", "jq14q18*Sp14*Sm18", "jq14q18*Sm14*Sp18", "jq87q88*Sp87*Sm88", "jq87q88*Sm87*Sp88", "jq97q98*Sp97*Sm98", "jq97q98*Sm97*Sp98", "jq1q2*Sp1*Sm2", "jq1q2*Sm1*Sp2", "jq112q126*Sp112*Sm126", "jq112q126*Sm112*Sp126", 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