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 C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
using namespace std;

using ll = long long;
#define int long long

// [a -> b-1]
#define reps(i, a, b) for (int i = (int)(a); i < (int)(b); i++)
// [0 -> a-1]
#define rep(i, a) reps(i, 0, (a))
// [a-1 -> b]
#define rreps(i, a, b) for (int i = (int)((a)-1); i >= (int)(b); i--)
// [a-1 -> 0]
#define rrep(i, a)a, rreps(i,  0)
#define all(v) (v).begin(), (v).end()
// next_permutation(all(v))
#define PERM(v) next_permutation(all(v))
/*sort(all(v));
 * (v).erase(unique(all(v)), v.end())*/
#define UNIQUE(v)\
	sort(all(v));\
	(v).erase(unique(all(v)), v.end())
#define MINV(v) min_element(all(v))
#define MAXV(v) max_element(all(v))
#define MIN3(a, b, c) min(min(a, b), c)
#define MIN4(a, b, c, d) min(MIN3(a, b, c), d)
#define MIN5(a, b, c, d, e) min(MIN4(a, b, c, d), e)
#define MIN6(a, b, c, d, e, f) min(MIN5(a, b, c, d, e), f)
#define MAX3(a, b, c) max(max(a, b), c)
#define MAX4(a, b, c, d) max(MAX3(a, b, c), d)
#define MAX5(a, b, c, d, e) max(MAX4(a, b, c, d), e)
#define MAX6(a, b, c, d, e, f) max(MAX5(a, b, c, d, e), f)
// b is [a, c)
#define RANGE(a, b, c) ((a) <= (b) && (b) < (c))
// c is [a, e) && d is [b, f)
#define RANGE2D(a, b, c, d, e, f) (RANGE((a), (c), (e)) && RANGE((b), (d), (f)))
#define chmin(a, b) a = min(a, (b))
#define chmin3(a, b, c) a = MIN3(a, (b), (c))
#define chmin4(a, b, c, d) a = MIN4(a, (b), (c), (d))
#define chmin5(a, b, c, d, e) a = MIN5(a, (b), (c), (d), (e))
#define chmin6(a, b, c, d, e, f) a = MIN6(a, (b), (c), (d), (e), (f))
#define chmax(a, b) a = max(a, (b))
#define chmax3(a, b, c) a = MAX3(a, (b), (c))
#define chmax4(a, b, c, d) a = MAX4(a, (b), (c), (d))
#define chmax5(a, b, c, d, e) a = MAX5(a, (b), (c), (d), (e))
#define chmax6(a, b, c, d, e, f) a = MAX6(a, (b), (c), (d), (e), (f))
#define fcout cout << fixed << setprecision(15)
#define YES(f) cout << ((f) ? YES_STR : NO_STR) << endl;

const long long MOD = 1000000007;

template<int mod> struct ModInt {
	using ll = long long;
	int x;
	template<class T>
	ModInt(T a) {
		x = a % mod;
		if (x < 0) {
			x += mod;
		}
	}
	ModInt() : x(0) {}
	inline ModInt& operator+=(const ModInt& rhs)
	{
		(*this) += rhs.x;
		return *this;
	}
	template<class T>
	inline ModInt& operator+=(const T rhs)
	{
		x += rhs % mod;
		if (x < 0) x += mod;
		x %= mod;
		return *this;
	}
	inline ModInt& operator-=(const ModInt& rhs)
	{
		(*this) -= rhs.x;
		return *this;
	}
	template<class T>
	inline ModInt& operator-=(const T rhs)
	{
		x -= rhs % mod;
		if (x < 0) x += mod;
		x %= mod;
		return *this;
	}
	inline ModInt& operator*=(const ModInt& rhs)
	{
		(*this) *= rhs.x;
		return *this;
	}
	template<class T>
	inline ModInt& operator*=(const T rhs)
	{
		ll res = (ll) x * (rhs % mod);
		x = res % mod;
		if (x < 0) x += mod;
		return *this;
	}
	inline ModInt& operator/=(const ModInt& rhs)
	{
		(*this) /= rhs.x;
		return *this;
	}
	template<class T>
	inline ModInt& operator/=(const T rhs)
	{
		int t = rhs % mod;
		if (t < 0) t += mod;
		ll res = modpow(t);
		(*this) *= res;
		return *this;
	}
	inline ModInt& operator=(const ModInt& rhs)
	{
		(*this) = rhs.x;
		return *this;
	}
	template<class T>
	inline ModInt& operator=(const T rhs)
	{
		x = rhs % mod;
		if (x < 0) x += mod;
		return *this;
	}
	inline int operator==(const ModInt& rhs) const
	{
		return (*this) == rhs.x;
	}
	template<class T>
	inline int operator==(const T rhs) const
	{
		ModInt t(rhs);
		return (*this).x == t.x;
	}
	inline int operator!=(const ModInt& rhs) const
	{
		return (*this) != rhs.x;
	}
	inline int operator!=(const int rhs) const
	{
		ModInt t(rhs);
		return (*this).x != t.x;
	}
	inline ModInt operator++(signed unused)
	{
		ModInt res((*this).x);
		++(*this);
		return res;
	}
	inline ModInt& operator++()
	{
		(*this) += 1;
		return (*this);
	}
	inline ModInt operator--(signed unused)
	{
		ModInt res((*this).x);
		--(*this);
		return res;
	}
	inline ModInt& operator--()
	{
		(*this) -= 1;
		return (*this);
	}
	inline ModInt operator+() const
	{
		return (*this);
	}
	inline ModInt operator-() const
	{
		return (*this).x ? ModInt(mod - (*this).x) : ModInt(0);
	}
	template<class T>
	int modpow(const T val, int p = mod - 2)
	{
		if (p == 0) return 1;
		if (p % 2) return (long long) val * modpow(val, p-1) % mod;
		long long t = modpow(val, p/2);
		int res = t * t % mod;
		return res;
	}
	operator int() const
	{
		return x;
	}
	friend ostream& operator<<(ostream& lhs, const ModInt& rhs)
	{
		lhs << rhs.x;
		return lhs;
	}
	friend istream& operator>>(istream& lhs, ModInt& rhs)
	{
		long long t;
		lhs >> t;
		rhs.x = t % mod;
		if (rhs.x < 0) rhs += mod;
		return lhs;
	}
	friend const ModInt operator+(const ModInt& lhs, const ModInt& rhs)  {return ModInt(lhs) += rhs;}
	template<class T>
	friend const ModInt operator+(const ModInt& lhs, const T rhs)        {return ModInt(lhs) += rhs;}
	template<class T>
	friend const ModInt operator+(T lhs, const ModInt& rhs)              {return ModInt(lhs) += rhs;}
	friend const ModInt operator-(const ModInt& lhs, const ModInt& rhs)  {return ModInt(lhs) -= rhs;}
	template<class T>
	friend const ModInt operator-(const ModInt& lhs, const T rhs)        {return ModInt(lhs) -= rhs;}
	template<class T>
	friend const ModInt operator-(T lhs, const ModInt& rhs)              {return ModInt(lhs) -= rhs;}
	friend const ModInt operator*(const ModInt& lhs, const ModInt& rhs)  {return ModInt(lhs) *= rhs;}
	template<class T>
	friend const ModInt operator*(const ModInt& lhs, const T rhs)        {return ModInt(lhs) *= rhs;}
	template<class T>
	friend const ModInt operator*(T lhs, const ModInt& rhs)              {return ModInt(lhs) *= rhs;}
	friend const ModInt operator/(const ModInt& lhs, const ModInt& rhs)  {return ModInt(lhs) /= rhs;}
	template<class T>
	friend const ModInt operator/(const ModInt& lhs, const T rhs)        {return ModInt(lhs) /= rhs;}
	template<class T>
	friend const ModInt operator/(T lhs, const ModInt& rhs)              {return ModInt(lhs) /= rhs;}
	template<class T>
	friend const int    operator==(T lhs, const ModInt& rhs)             {return ModInt(lhs) == rhs;}
	template<class T>
	friend const int    operator!=(T lhs, const ModInt& rhs)             {return ModInt(lhs) != rhs;}
};
using modint = ModInt<1000000007>;

void solve(std::string S) {
	int N = S.length();
	vector<vector<modint>> dp(N+1, vector<modint>(13, 0));
	dp[0][0] = 1;
	vector<int> A(N, 1);
	reps(i, 1, N) {
		A[i] = (A[i-1] * 10) % 13;
	}
	reverse(all(A));
	reps(i, 1, N + 1) {
		rep(j, 13) {
			if (S[i-1] == '?') {
				rep(k, 10) {
					dp[i][(k * A[i-1] + j) % 13] += dp[i-1][j];
				}
			} else {
				int k = S[i-1] - '0';
				dp[i][(k * A[i-1] + j) % 13] += dp[i-1][j];
			}
		}
	}
	cout << dp[N][5] << endl;
}

signed main() {
	std::string S;
	std::cin >> S;
	solve(S);
	return 0;
}