-------------------------------------------------------------------------------- Two-loop five-point massless QCD amplitudes within the IBP approach Authors: H. A. Chawdhry, M. A. Lim, A. D. Mitov (2018) Contact: herschel@hep.phy.cam.ac.uk malim@hep.phy.cam.ac.uk adm74@cam.ac.uk When using these results, please cite the paper: Chawdhry, Lim, Mitov (2018) These and further results are available here: http://www.precision.hep.phy.cam.ac.uk/results/amplitudes/ -------------------------------------------------------------------------------- #----------IMPORTANT: Restoration of dimensionful parameter s12: In our calculations we have set s12=1. This means that after retrieving the projection of any integral onto a master integral, one must restore an overall power of s12 by comparing the mass dimensions of the two sides of the equation. #----------Momentum variables: (see figure in paper) Incoming momenta: p1, p2 Outgoing momenta: p3, p4, p5 Constraints: p1 + p2 = p3 + p4 + p5 p_i^2 = 0 #----------Kinematic invariants: s12 := (p1 + p2)^2 s23 := (p2 + p3)^2 s34 := (p3 + p4)^2 s45 := (p4 + p5)^2 s51 := (p5 + p1)^2 #----------IBP variables: (all results are expressed in terms of these variables) a := s23/s12 b := s34/s12 c := s45/s12 d := s51/s12 e := D (the number of space-time dimensions) #----------Master integrals: mastersC1={ C[0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0], C[0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0], C[0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0], C[0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0], C[0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0], C[1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0], C[0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0], C[0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0], C[0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0], C[0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0], C[0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0], C[1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0], C[1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0], C[1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0], C[1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0], C[1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0], C[0, 0, 0, 1, 1, 1, 0, 1, 1, 0, 0], C[0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0], C[0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 0], C[0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0], C[0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0], C[0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0], C[0, 1, 1, 1, 0, 0, 0, 1, 1, 0, 0], C[0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0], C[0, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0], C[0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0], C[1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0], C[1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0], C[1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0], C[1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0], C[1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0], C[1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0], C[1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0], C[-1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 0], C[-1, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0], C[1, -1, 0, 1, 1, 1, 0, 1, 0, 0, 0], C[0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0], C[0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0], C[0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0], C[0, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0], C[1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 0], C[1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0], C[1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 0], C[1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0], C[1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0], C[-1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0], C[-1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0], C[1, -1, 0, 1, 1, 1, 0, 1, 1, 0, 0], C[1, -1, 1, 1, 1, 0, 0, 1, 1, 0, 0], C[0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0], C[1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0], C[1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0], C[1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0], C[-1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0], C[0, 1, 1, 1, 1, 1, -1, 1, 1, 0, 0], C[1, 1, -1, 1, 1, 1, 0, 1, 1, 0, 0], C[1, 1, 0, 1, 1, 1, -1, 1, 1, 0, 0], C[1, 1, 1, 1, 1, 1, -1, 0, 1, 0, 0], C[1, 1, 1, 1, 1, 1, -1, 1, 0, 0, 0], C[1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0], C[1, 1, 1, 1, 1, 1, -1, 1, 1, 0, 0], C[1, 1, 1, 1, 1, 1, 0, 1, 1, 0, -1]}; mastersC2={ C[0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0], C[0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0], C[0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0], C[0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0], C[1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0], C[1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0], C[0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0], C[0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0], C[0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1], C[0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1], C[1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0], C[0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0], C[1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0], C[0, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0], C[-1, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0], C[0, 1, 1, 1, 0, 0, 0, 1, 1, 0, 0], C[1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0], C[0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0], C[0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0], C[0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 1], C[0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1], C[0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 1], C[1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0], C[1, -1, 1, 1, 1, 0, 0, 1, 1, 0, 0], C[0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0], C[-1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0], C[0, 1, 1, 1, 0, 0, 0, 1, 1, 0, 1], C[-1, 1, 1, 1, 0, 0, 0, 1, 1, 0, 1]}; mastersC3={ C[1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0], C[0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0], C[1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0], C[1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0], C[1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0], C[0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1], C[1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0], C[1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0], C[1, -1, 0, 1, 1, 1, 0, 1, 0, 0, 0], C[1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1]}; mastersB1={ B[0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0], B[0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0], B[0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0], B[1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0], B[0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0], B[0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0], B[0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0], B[1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0], B[0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0], B[1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0], B[1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0], B[1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0], B[1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0], B[1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0], B[1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0], B[0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0], B[0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0], B[1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0], B[0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0], B[1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0], B[0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0], B[1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0], B[1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0], B[1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0], B[1, 1, -1, 1, 1, 0, 1, 0, 0, 0, 0], B[1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0], B[0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0], B[1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0], B[1, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0], B[1, 1, -1, 1, 0, 1, 1, 0, 0, 0, 0], B[0, 1, 1, 1, 0, 1, 1, 0, 0, 0, 0], B[0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0], B[0, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0], B[0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0], B[1, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0], B[1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0], B[1, 1, -1, 1, 0, 1, 0, 1, 0, 0, 0], B[1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0], B[0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0], B[0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0], B[1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0], B[0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0], B[0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0], B[-1, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0], B[1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0], B[1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0], B[1, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0], B[1, -1, 1, 0, 1, 0, 1, 1, 0, 0, 0], B[0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 0], B[1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0], B[1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0], B[1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0], B[0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0], B[0, 0, 1, 0, 1, 1, 1, 1, 0, 0, 0], B[-1, 0, 1, 0, 1, 1, 1, 1, 0, 0, 0], B[1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0], B[1, 1, 1, 1, 1, -1, 1, 0, 0, 0, 0], B[1, 1, 1, 1, 0, 1, 1, 0, 0, 0, 0], B[1, 1, 1, 1, -1, 1, 1, 0, 0, 0, 0], B[1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0], B[1, 1, -1, 1, 1, 1, 1, 0, 0, 0, 0], B[0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0], B[1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0], B[1, 1, 1, 1, -1, 1, 0, 1, 0, 0, 0], B[1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0], B[1, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0], B[0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0], B[-1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0], B[1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 0], B[1, 1, 1, -1, 1, 0, 1, 1, 0, 0, 0], B[1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0], B[1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0], B[1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0], B[1, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0], B[1, 1, -1, 1, 0, 1, 1, 1, 0, 0, 0], B[1, 0, 1, 0, 1, 1, 1, 1, 0, 0, 0], B[1, -1, 1, 0, 1, 1, 1, 1, 0, 0, 0], B[0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0], B[-1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0], B[1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0], B[0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0], B[-1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0], B[1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0], B[1, 1, 1, 1, 1, 1, 1, -1, 0, 0, 0], B[1, 1, 1, 1, 1, 1, 1, 0, -1, 0, 0], B[1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0], B[1, 1, 1, 1, 1, 1, -1, 1, 0, 0, 0], B[1, 1, 1, 1, 1, 1, 0, 1, -1, 0, 0], B[1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 0], B[1, 1, 1, 1, 1, -1, 1, 1, 0, 0, 0], B[1, 1, 1, 1, 1, 0, 1, 1, -1, 0, 0], B[1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0], B[1, 1, 1, 1, -1, 1, 1, 1, 0, 0, 0], B[1, 1, 1, 1, 0, 1, 1, 1, -1, 0, 0], B[1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0], B[1, 1, 1, -1, 1, 1, 1, 1, 0, 0, 0], B[1, 1, 1, 0, 1, 1, 1, 1, -1, 0, 0], B[1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 0], B[1, 1, -1, 1, 1, 1, 1, 1, 0, 0, 0], B[1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0], B[1, -1, 1, 1, 1, 1, 1, 1, 0, 0, 0], B[0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0], B[-1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0], B[0, 1, 1, 1, 1, 1, 1, 1, -1, 0, 0], B[1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0], B[1, 1, 1, 1, 1, 1, 1, 1, -1, 0, 0], B[1, 1, 1, 1, 1, 1, 1, 1, 0, -1, 0], B[1, 1, 1, 1, 1, 1, 1, 1, 0, 0, -1], B[1, 1, 1, 1, 1, 1, 1, 1, -2, 0, 0], B[1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 0], B[1, 1, 1, 1, 1, 1, 1, 1, -1, 0, -1], B[1, 1, 1, 1, 1, 1, 1, 1, 0, -2, 0], B[1, 1, 1, 1, 1, 1, 1, 1, 0, -1, -1]}; mastersB2={ B[0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0], B[0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0], B[1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0], B[0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0], B[1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0], B[0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0], B[1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0], B[0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1], B[1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0], B[1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0], B[1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0], B[0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1], B[0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1], B[0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1], B[0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1], B[0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1], B[1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0], B[1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0], B[1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0], B[1, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0], B[1, 1, -1, 1, 0, 1, 1, 0, 0, 0, 0], B[0, 1, 1, 1, 0, 1, 1, 0, 0, 0, 0], B[1, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0], B[1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0], B[1, 1, -1, 1, 0, 1, 0, 1, 0, 0, 0], B[1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0], B[0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0], B[1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0], B[1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0], B[1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0], B[0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0], B[1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1], B[1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1], B[0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 1], B[1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1], B[1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1], B[0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1], B[1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1], B[1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1], B[0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1], B[-1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1], B[1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1], B[0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1], B[-1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1], B[1, 1, 1, 1, 0, 1, 1, 0, 0, 0, 0], B[1, 1, 1, 1, -1, 1, 1, 0, 0, 0, 0], B[1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0], B[1, 1, 1, 1, -1, 1, 0, 1, 0, 0, 0], B[1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0], B[1, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0], B[1, 1, -1, 1, 0, 1, 1, 1, 0, 0, 0], B[1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 1], B[1, 1, 1, 1, 0, -1, 1, 0, 0, 0, 1], B[1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1], B[1, -1, 1, 1, 0, 1, 0, 1, 0, 0, 1], B[1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1], B[1, 1, 1, -1, 0, 0, 1, 1, 0, 0, 1], B[1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1], B[1, -1, 1, 0, 0, 1, 1, 1, 0, 0, 1], B[0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1], B[-1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1], B[0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1], B[1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0], B[1, 1, 1, 1, -1, 1, 1, 1, 0, 0, 0], B[1, 1, 1, 1, 0, 1, 1, 1, -1, 0, 0], B[1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1], B[1, 1, 1, -1, 0, 1, 1, 1, 0, 0, 1], B[1, 1, 1, 0, -1, 1, 1, 1, 0, 0, 1], B[1, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1], B[1, 1, -1, 1, 0, 1, 1, 1, 0, 0, 1], B[0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1], B[-1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1], B[1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1], B[1, 1, 1, 1, -1, 1, 1, 1, 0, 0, 1], B[1, 1, 1, 1, -2, 1, 1, 1, 0, 0, 1]};