Problem:
Score : 400 points

Problem Statement

Given is a string S. Each character in S is either a digit (0, ..., 9) or ?.

Among the integers obtained by replacing each occurrence of ? with a digit, how many have a remainder of 5 when divided by 13? An integer may begin with 0.

Since the answer can be enormous, print the count modulo 10^9+7.

Constraints

S is a string consisting of digits (0, ..., 9) and ?.

1 \leq |S| \leq 10^5

Input

Input is given from Standard Input in the following format:

S

Output

Print the number of integers satisfying the condition, modulo 10^9+7.

Sample Input 1

??2??5

Sample Output 1

768

For example, 482305, 002865, and 972665 satisfy the condition.

Sample Input 2

?44

Sample Output 2

1

Only 044 satisfies the condition.

Sample Input 3

7?4

Sample Output 3

0

We may not be able to produce an integer satisfying the condition.

Sample Input 4

?6?42???8??2??06243????9??3???7258??5??7???????774????4?1??17???9?5?70???76???

Sample Output 4

153716888

Solution in Python (3.4.3) (judge verdict: Time Limit Exceeded)

from sys import exit, stderr, stdin
input = stdin.readline
# setrecursionlimit(10**7)


# def debug(var, name="hoge"):
#     print(name +":" + str(type(var)) + " = " + repr(var), file=stderr)
#     return


def main():
    MOD = 10**9 + 7
    S = list(input()[:-1])
    L = len(S)
    modsum = 0
    # 余り
    memo_prev = [0 for _ in range(13)]
    memo_prev[0] = 1
    memo = [0 for _ in range(13)]

    for i in range(L):
        memo = [0 for _ in range(13)]
        # 数字なら以前までの余りにたす
        if S[i].isnumeric():
            for m in range(13):
                cur = (10*m+int(S[i]))%13
                memo[cur] += memo_prev[m]
        # ?なら1~10の余りのケース全てをためす
        else:
            for n in range(10):
                for m in range(13):
                    cur = (10*m+n)%13
                    memo[cur] += memo_prev[m]
                    memo[cur] %= MOD
        memo_prev = memo.copy()
    print(memo[5])


if __name__ == "__main__":
    main()