Ositus

import math
string = input()

n = len(string)

parts = []

for i in range(1 << (n-1)):
    lastcut = 0
    p = []
    for k in range(n-1):
        if (1 << k) & i != 0:
            p.append(string[lastcut:k+1])
            lastcut = k + 1
    p.append(string[lastcut:])
    parts.append(p)

ans = len(parts)
# print(ans)
for l in parts:
    for x in l:
        if len(set(x)) < len(x):
            ans -= 1
            break

print(ans)

Test 1

Group: 1, 2, 3

Verdict: ACCEPTED

Test 2

Group: 1, 2, 3

Verdict: ACCEPTED

Test 3

Group: 1, 2, 3

Verdict: ACCEPTED

Test 4

Group: 1, 2, 3

Verdict: ACCEPTED

Test 5

Group: 2, 3

Verdict: TIME LIMIT EXCEEDED

Test 6

Group: 3

Verdict: TIME LIMIT EXCEEDED

Test 7

Group: 3

Verdict: TIME LIMIT EXCEEDED