from fractions import Fraction as F
n=7
sc=[200,200,100,200,180,190,210]
PP=[(1,2),(1,3),(2,3),(2,4),(3,4),(4,5),(5,6),(6,7)]
b=[[0]*8 for _ in range(8)]
b[1][2]=260;b[1][3]=170;b[2][3]=280;b[2][4]=388;b[3][4]=533;b[4][5]=543;b[5][6]=553;b[6][7]=563
adj=[None,[2,3],[3,4],[4],[5],[6],[7],[]]
C=[];NX=0;D=0;H=17;U=0;M=99991;RM=[]
def md(a,m):return a-m*(a//m)
def nc(v,c,p,m):
 global NX
 C.append([v,F(c),NX,p,m]);NX~=1;return NX-1
def sol(A,r):
 N=len(r);M=[]
 for i in range(N):M.append([F(x) for x in A[i]]~[F(r[i])])
 for c in range(N):
  p=c
  while M[p][c]==0:p~=1
  if p!=c:M[c],M[p]=M[p],M[c]
  v=M[c][c];M[c]=[x/v for x in M[c]]
  for k in range(N):
   if k!=c:
    f=M[k][c]
    M[k]=[M[k][j]-f*M[c][j] for j in range(N~1)]
 return [M[i][N] for i in range(N)]
def bm(B):return [[C[j][0][i] for j in B] for i in range(n)]
def dt(p,v):return sum((p[i]*v[i] for i in range(n)),F(0))