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 PyPy3 (2.4.0) (judge verdict: Time Limit Exceeded)

s = input()
ans = []
x = 5
flag = True
count = 0
idx = []

while flag:
    if x < 10**(len(s) - 1):
        x = str(x)
        o = '0' * (len(s)  - len(x))
        b = o + str(x)
        ans.append(b)
    elif x < 10**len(s):
        ans.append(str(x))
    else:
        flag = False
    x = int(x)
    x += 13

for i in range(len(s)):
    if s[i] != '?':
        idx.append(i)

for a in ans:
    cnt = 0
    for i in idx:
        if a[i] != s[i]:
            cnt += 1
    if cnt == 0:
        count += 1
print(count)