Problem: You are given a figure on a grid representing stairs consisting of 7 steps. The width of the stair on height i is wi squares. Formally, the figure is created by consecutively joining rectangles of size wi × i so that the wi sides lie on one straight line. Thus, for example, if all wi = 1, the figure will look like that (different colors represent different rectangles):

<image>

And if w = {5, 1, 0, 3, 0, 0, 1}, then it looks like that:

<image>

Find the number of ways to color some borders of the figure's inner squares so that no square had all four borders colored. The borders of the squares lying on the border of the figure should be considered painted. The ways that differ with the figure's rotation should be considered distinct. 

Input

The single line of the input contains 7 numbers w1, w2, ..., w7 (0 ≤ wi ≤ 105). It is guaranteed that at least one of the wi's isn't equal to zero.

Output

In the single line of the output display a single number — the answer to the problem modulo 109 + 7.

Examples

Input

0 1 0 0 0 0 0


Output

1


Input

0 2 0 0 0 0 0


Output

7


Input

1 1 1 0 0 0 0


Output

9


Input

5 1 0 3 0 0 1


Output

411199181

Note

All the possible ways of painting the third sample are given below:

<image>

Solution (in JAVA):

Solution:
import java.io.*;

public class CF498E {

    final static long MOD = 1000000007;

    static long[][] mul(long[][] a, long[][] b) {
        long[][] c = new long[a.length][a.length];
        for (int i = 0; i < a.length; ++i) {
            for (int j = 0; j < a.length; ++j) {
                for (int k = 0; k < a.length; ++k) {
                    c[i][j] = (c[i][j] + a[i][k] * b[k][j]) % MOD;
                }
            }
        }
        return c;
    }

    static long[][] pow(long[][] a, long pow) {
        long[][] r = new long[a.length][a.length];
        for (int i = 0; i < a.length; ++i) {
            r[i][i] = 1;
        }
        while (pow > 0) {
            if (pow % 2 == 1) {
                r = mul(r, a);
            }
            pow /= 2;
            a = mul(a, a);
        }
        return r;
    }

    static long[][] mat(int n) {
        long[][] r = new long[1 << n][1 << n];
        for (int mask0 = 0; mask0 < 1 << n; ++mask0) {
            for (int mask1 = 0; mask1 < 1 << n; mask1 += 2) {
                for (int mask2 = 0; mask2 < 1 << n; ++mask2) {
                    int mask = mask0 | mask1 | (mask1 >> 1) | mask2;
                    if ((mask & ((1 << n) - 1)) == ((1 << n) - 1)) {
                        r[mask0][mask2]++;
                    }
                }
            }
        }
        return r;
    }

    public static void solve(Input in, PrintWriter out) throws IOException {
        long[] v = new long[1];
        v[0] = 1;
        for (int h = 1; h <= 7; ++h) {
            int w = in.nextInt();
            if (w != 0) {
                long[][] a = pow(mat(h), w);
                long[] v1 = new long[1 << h];
                for (int i = 0; i < v.length; ++i) {
                    for (int j = 0; j < v1.length; ++j) {
                        v1[j] = (v1[j] + v[i] * a[i][j]) % MOD;
                    }
                }
                v = v1;
            }
        }
        out.println(v[0]);
    }

    public static void main(String[] args) throws IOException {
        PrintWriter out = new PrintWriter(System.out);
        solve(new Input(new BufferedReader(new InputStreamReader(System.in))), out);
        out.close();
    }

    static class Input {
        BufferedReader in;
        StringBuilder sb = new StringBuilder();

        public Input(BufferedReader in) {
            this.in = in;
        }

        public Input(String s) {
            this.in = new BufferedReader(new StringReader(s));
        }

        public String next() throws IOException {
            sb.setLength(0);
            while (true) {
                int c = in.read();
                if (c == -1) {
                    return null;
                }
                if (" \n\r\t".indexOf(c) == -1) {
                    sb.append((char)c);
                    break;
                }
            }
            while (true) {
                int c = in.read();
                if (c == -1 || " \n\r\t".indexOf(c) != -1) {
                    break;
                }
                sb.append((char)c);
            }
            return sb.toString();
        }

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

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

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