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 $10^9+7$.