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.InputStreamReader;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.StringTokenizer;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
	public static void main(String[] args) {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		FastScanner in = new FastScanner(inputStream);
		PrintWriter out = new PrintWriter(outputStream);
		TaskE solver = new TaskE();
		solver.solve(1, in, out);
		out.close();
	}
}

class TaskE {
	public void solve(int testNumber, FastScanner in, PrintWriter out) {
		int[] w = new int[7];
		for (int i = 0; i < 7; i++) {
			w[i] = in.nextInt();
		}
		int[] v = {0, 1};
		for (int i = 1; i <= 7; i++) {
			int[][] m = genTransitions(i);
			m = pow(m, w[i - 1]);
			v = mul(m, v);
			int[] nv = new int[1<<(i + 1)];
			for (int j = 0; j < 1<<i; j++) {
				nv[j | (1<<i)] = v[j];
			}
			v = nv;
		}
		out.println(v[v.length - 1]);
	}

	final int MOD = (int)(1e9 + 7);

	private int[][] genTransitions(int n) {
		int[][] a = new int[1<<n][1<<n];
		for (int i = 0; i < 1<<n; i++) {
			for (int j = 0; j < 1<<n; j++) {
				int[][] d = new int[2][n + 1];
				d[1][0] = 1;
				for (int k = 1; k <= n; k++) {
					for (int prev = 0; prev < 2; prev++) {
						for (int cur = 0; cur < 2; cur++) {
							if (cur + prev + ((i >> (k-1)) & 1) + ((j >> (k-1)) & 1) < 4) {
								d[cur][k] += d[prev][k - 1];
							}
						}
					}
				}
				a[i][j] = d[1][n];
			}
		}
		return a;
	}

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

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

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

class FastScanner {

	private BufferedReader in;
	private StringTokenizer st;

	public FastScanner(InputStream stream) {
		in = new BufferedReader(new InputStreamReader(stream));
	}

	public String next() {
		while (st == null || !st.hasMoreTokens()) {
			try {
				String rl = in.readLine();
				if (rl == null) {
					return null;
				}
				st = new StringTokenizer(rl);
			} catch (IOException e) {
				throw new RuntimeException(e);
			}
		}
		return st.nextToken();
	}

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

}