from collections import defaultdict
n = 3
h = defaultdict(int)
xs = list(range(1, n + 1))
q = [(xs, 0)]

while q:
    e, c = q.pop()
    if c == n:
        h[tuple(e)] += 1
    if c < n:
        for i in range(n):
            x = e[:]
            x[c], x[i] = x[i], x[c]
            q.append((x, c + 1))
print(h)