Digits Parade

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.

Examples

Input

??2??5

Output

768

Input

?44

Output

1

Input

7?4

Output

0

Input

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

Output

153716888

inputFormat

Input

Input is given from Standard Input in the following format:

S

outputFormat

Output

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

Examples

Input

??2??5

Output

768

Input

?44

Output

1

Input

7?4

Output

0

Input

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

Output

153716888

样例

7?4

0