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: Runtime Error)

MOD = 10 ** 9 + 7

s = str(input())
sl = list(s)
si = list(map(int,s))

cur = [0] * 13

if s[0] != "?":
    cur[si[0]] = 1
else:
    for j in range(10):
        cur[j] = 1

for i in range(1,len(s)):
    pre = cur[:]
    cur = [0] * 13
    if s[i] != "?":
        for j in range(13):
            q = (j * 10 + si[i]) % 13
            cur[q] += pre[j] % MOD
    else:
        for j in range(13):
            for k in range(10):
                p = (j * 10 + k) % 13
                cur[p] += pre[j] % MOD

print(cur[5] % MOD)