Game "Minesweeper 1D" is played on a line of squares, the line's height is 1 square, the line's width is n squares. Some of the squares contain bombs. If a square doesn't contain a bomb, then it contains a number from 0 to 2 — the total number of bombs in adjacent squares.

For example, the correct field to play looks like that: 001*2***101*. The cells that are marked with "*" contain bombs. Note that on the correct field the numbers represent the number of bombs in adjacent cells. For example, field 2* is not correct, because cell with value 2 must have two adjacent cells with bombs.

Valera wants to make a correct field to play "Minesweeper 1D". He has already painted a squared field with width of n cells, put several bombs on the field and wrote numbers into some cells. Now he wonders how many ways to fill the remaining cells with bombs and numbers are there if we should get a correct field in the end.

Input

The first line contains sequence of characters without spaces s1s2... sn (1 ≤ n ≤ 106), containing only characters "*", "?" and digits "0", "1" or "2". If character si equals "*", then the i-th cell of the field contains a bomb. If character si equals "?", then Valera hasn't yet decided what to put in the i-th cell. Character si, that is equal to a digit, represents the digit written in the i-th square.

Output

Print a single integer — the number of ways Valera can fill the empty cells and get a correct field.

As the answer can be rather large, print it modulo 1000000007 (109 + 7).

Examples

Input

?01???


Output

4


Input

?


Output

2


Input

**12


Output

0


Input

1


Output

0

Note

In the first test sample you can get the following correct fields: 001**1, 001***, 001*2*, 001*10.

import java.io.BufferedReader;
import java.io.File;
import java.io.FileInputStream;
import java.io.FileNotFoundException;
import java.io.FileOutputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.HashMap;
import java.util.HashSet;
import java.util.PriorityQueue;
import java.util.Stack;
import java.util.StringTokenizer;
import java.util.TreeSet;

/**
 *
 *
 * 3 2 3 5
 * -2 -1 4 -1 2 7 3
 *
 * 10 1 -10617 30886 -7223 -63085 47793 -61665 -14614 60492 16649 -58579 3 8 1
 * 10 4 7 1 7 3 7
 *
 * 22862 -34877
 *
 * @author pttrung
 */
public class D {

    public static long MOD = 1000000007;
    public static long[][] dp;

    public static void main(String[] args) throws FileNotFoundException {
        PrintWriter out;
        Scanner in = new Scanner();
        //out = new PrintWriter(new FileOutputStream(new File("output.txt")));
        out = new PrintWriter(System.out);
        String line = in.nextLine();
        int n = line.length();
        long[][][] dp = new long[2][3][n];

        for (int i = n - 1; i >= 0; i--) {
            if (line.charAt(i) == '*') {
                dp[0][0][i] = 0;
                dp[0][1][i] = (i + 1 < n) ? dp[1][2][i + 1] : 1;
                dp[0][2][i] = (i + 1 < n) ? dp[1][2][i + 1] : 1;
                dp[1][0][i] = 0;
                dp[1][1][i] = (i + 1 < n) ? dp[1][2][i + 1] : 1;
                dp[1][2][i] = (i + 1 < n) ? dp[1][2][i + 1] : 1;
            } else if (line.charAt(i) == '?') {
                dp[0][0][i] = (i + 1 < n) ? dp[0][2][i + 1] : 1;
                dp[0][1][i] = (i + 1 < n) ? dp[1][2][i + 1] : 1;
                dp[0][2][i] = (i + 1 < n) ? (dp[0][2][i + 1] + dp[1][2][i + 1]) % MOD : 2;
                dp[1][0][i] = (i + 1 < n) ? dp[0][2][i + 1] : 1;
                dp[1][1][i] = (i + 1 < n) ? dp[1][2][i + 1] : 1;
                dp[1][2][i] = (i + 1 < n) ? (dp[0][2][i + 1] + dp[1][2][i + 1]) % MOD : 2;
            } else if (line.charAt(i) == '0') {
                dp[0][0][i] = (i + 1 < n) ? dp[0][0][i + 1] : 1;
                dp[0][1][i] = 0;
                dp[0][2][i] = (i + 1 < n) ? dp[0][0][i + 1] : 1;
                dp[1][0][i] = 0;
                dp[1][1][i] = 0;
                dp[1][2][i] = 0;
            } else if (line.charAt(i) == '1') {
                dp[0][0][i] = (i + 1 < n) ? dp[0][1][i + 1] : 0;
                dp[0][1][i] = 0;
                dp[0][2][i] = (i + 1 < n) ? dp[0][1][i + 1] : 0;
                dp[1][0][i] = (i + 1 < n) ? dp[0][0][i + 1] : 1;
                dp[1][1][i] = 0;
                dp[1][2][i] = (i + 1 < n) ? dp[0][0][i + 1] : 1;
            } else {
                dp[0][0][i] = 0;
                dp[0][1][i] = 0;
                dp[0][2][i] = 0;
                dp[1][0][i] = (i + 1 < n) ? dp[0][1][i + 1] : 0;
                dp[1][1][i] = 0;
                dp[1][2][i] = (i + 1 < n) ? dp[0][1][i + 1] : 0;
            }
        }


        out.println(dp[0][2][0]);

        out.close();
    }

    
    public static boolean nextPer(int[] data) {
        int i = data.length - 1;
        while (i > 0 && data[i] < data[i - 1]) {
            i--;
        }
        if (i == 0) {
            return false;
        }
        int j = data.length - 1;
        while (data[j] < data[i - 1]) {
            j--;
        }
        int temp = data[i - 1];
        data[i - 1] = data[j];
        data[j] = temp;
        Arrays.sort(data, i, data.length);
        return true;
    }

    public static int digit(long n) {
        int result = 0;
        while (n > 0) {
            n /= 10;
            result++;
        }
        return result;
    }

    public static double dist(long a, long b, long x, long y) {
        double val = (b - a) * (b - a) + (x - y) * (x - y);
        val = Math.sqrt(val);
        double other = x * x + a * a;
        other = Math.sqrt(other);
        return val + other;








    }

    public static class Point implements Comparable<Point> {

        int x, y;

        public Point(int start, int end) {
            this.x = start;
            this.y = end;
        }

        @Override
        public int hashCode() {
            int hash = 5;
            hash = 47 * hash + this.x;
            hash = 47 * hash + this.y;
            return hash;
        }

        @Override
        public boolean equals(Object obj) {
            if (obj == null) {
                return false;
            }
            if (getClass() != obj.getClass()) {
                return false;
            }
            final Point other = (Point) obj;
            if (this.x != other.x) {
                return false;
            }
            if (this.y != other.y) {
                return false;
            }
            return true;
        }

        @Override
        public int compareTo(Point o) {
            return x - o.x;
        }
    }

    public static class FT {

        int[] data;

        FT(int n) {
            data = new int[n];
        }

        public void update(int index, int value) {
            while (index < data.length) {
                data[index] += value;
                index += (index & (-index));
            }
        }

        public int get(int index) {
            int result = 0;
            while (index > 0) {
                result += data[index];
                index -= (index & (-index));
            }
            return result;

        }
    }

    public static long gcd(long a, long b) {
        if (b == 0) {
            return a;
        }
        return gcd(b, a % b);
    }

    public static long pow(long a, long b) {
        if (b == 0) {
            return 1;
        }
        if (b == 1) {
            return a;
        }
        long val = pow(a, b / 2);
        if (b % 2 == 0) {
            return val * val % MOD;
        } else {
            return val * (val * a % MOD) % MOD;








        }
    }

    static class Scanner {

        BufferedReader br;
        StringTokenizer st;

        public Scanner() throws FileNotFoundException {
            // System.setOut(new PrintStream(new BufferedOutputStream(System.out), true));
            br = new BufferedReader(new InputStreamReader(System.in));
            //br = new BufferedReader(new InputStreamReader(new FileInputStream(new File("D-large.in"))));
        }

        public String next() {

            while (st == null || !st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (Exception e) {
                    throw new RuntimeException();
                }
            }
            return st.nextToken();
        }

        public long nextLong() {
            return Long.parseLong(next());
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

        public double nextDouble() {
            return Double.parseDouble(next());
        }

        public String nextLine() {
            st = null;
            try {
                return br.readLine();
            } catch (Exception e) {
                throw new RuntimeException();
            }
        }

        public boolean endLine() {
            try {
                String next = br.readLine();
                while (next != null && next.trim().isEmpty()) {
                    next = br.readLine();
                }
                if (next == null) {
                    return true;
                }
                st = new StringTokenizer(next);
                return st.hasMoreTokens();
            } catch (Exception e) {
                throw new RuntimeException();
            }
        }
    }
}
