import time
start = time.perf_counter()

def con(H):
    J = []
    Q = []
    W = []
    for i in H:
        for j in range(len(i)-1):
            Cop = i[::]
            y = i[j]+i[j+1]
            del Cop[j:j+2]
            Cop.insert(j,y)
            J.append(Cop)
    for i in J:
        y =(sorted("".join(str(j) for j in i)))
        Q.append("".join(y))
    T = list(set(Q))
    for i in T:
        y = [int(j) for j in i]
        W.append(y)
    return W

num = 5
K = [[1 for i in range(num)]]
count = 0
for i in range(len(K[0])-2):
    K = con(K)
    print(K)
    count = count + len(K)
print(count+1)
end = time.perf_counter()
print(end-start,"second")

4 + 1
3 + 2
3 + 1 + 1
2 + 2 + 1
2 + 1 + 1 + 1
1 + 1 + 1 + 1 + 1

3 + 1
2 + 2
2 + 1 + 1
1 + 1 + 1 + 1

(4 + 1)
(3 + 2)
3 + 1 (+ 1)
2 + 2 (+ 1)
2 + 1 + 1 (+ 1)
1 + 1 + 1 + 1 (+ 1)

(3 + 1)
(2 + 2)
2 + 1 (+ 1)
1 + 1 + 1 (+ 1)