``cache=[]
_build_dp=_build_dp
def _build_dp(last, s, array, rest, x, n):
    for j in reverse(len(n):
        if len(rest)>n:
            return 0
        if n==2:
            if s!=x:
                return 1
            else:
                return 0  
    _count=0
    if (len(rest)==n):
        for i in rest:
            if i!=s:
                _count+=_build_dp(s, i,  array, [ j for j in rest if j!=i ], x, n-1)
    else:
        for i in array:
            if i!=s:
                _count+=_build_dp(s, i,  array, [ j for j in rest if j!=i ], x, n-1)
        return _count