GREAT + SWERC = PORTO

We wanted a good SWERC in Porto this year and tried several ideas. One of them was turning the name into a word addition puzzle like the classic SEND+MORE=MONEY. In a word addition each letter stands for a single digit from 0 to 9, and substituting those digits has to make the addition correct. Different letters get different digits, and the leftmost letter of a word cannot be zero. In particular, a term made of a single letter cannot be zero.

Solving GREAT+SWERC=PORTO means giving G, S and P positive digits and giving R, E, A, T, W, C, O digits as well, so that every letter has a different digit and the sum is correct. Unlike SEND+MORE=MONEY, which has a single solution, GREAT+SWERC=PORTO has six solutions.

• T=7, E=3, W=9, G=1, A=0, P=4, S=2, C=8, R=6, O=5
• T=7, E=3, W=9, G=2, A=0, P=4, S=1, C=8, R=6, O=5
• T=8, E=5, W=1, G=3, A=7, P=9, S=6, C=4, R=0, O=2
• T=8, E=5, W=1, G=6, A=7, P=9, S=3, C=4, R=0, O=2
• T=9, E=5, W=2, G=1, A=8, P=7, S=6, C=4, R=0, O=3
• T=9, E=5, W=2, G=6, A=8, P=7, S=1, C=4, R=0, O=3

Having more than one solution makes it a poor puzzle to solve by hand, but a program handles it easily.

Given a word addition puzzle, compute the number of solutions. The count can be zero.

The first line contains an integer $n$. Each of the next $n$ lines contains one word of at most 10 letters. The first $n-1$ words are the terms to be added and the last line is the result. Words contain capital letters only. Words of different lengths are aligned to the right. For instance, in SEND+MORE=MONEY the D of the first word and the E of the second word sit in the same column as the Y of the last word. The length of the last word is at least the maximum length of the preceding words, and a puzzle involves at most ten distinct letters.

Print a single line with one integer, the number of solutions of the given word addition puzzle.

• $3 \le n \le 10$
• Each word has at most 10 letters, all capital.
• A puzzle involves at most 10 distinct letters.