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 Ruby (2.3.3) (judge verdict: Wrong Answer)

a = gets.strip.chomp.chars
p =[]
q = []
count = 0
a.each_with_index do |i,j|
  if i == "?"
    p << j
  else
    q << j
  end
end

# ?の数だけ強くなれるよ 桁数
n = 10 ** (p.size)

(0..n-1).each do |i|
  num_s  = format("%0*d",p.size, i)
  num_sa = num_s.strip.chomp.chars
  q.size.times do |j|
    num_sa.insert(q[j].to_i,a[q[j]])
  end
  d = num_sa.join("").to_i
  if d % 13 == 5
    count = count + 1
  end
end

puts (count % (10 ** 9 + 7))