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.util.Arrays;
import java.io.BufferedWriter;
import java.util.InputMismatchException;
import java.io.InputStream;
import java.util.NoSuchElementException;
import java.io.OutputStreamWriter;
import java.math.BigInteger;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.Writer;
import java.io.IOException;

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

class TaskE {
    public void solve(int testNumber, InputReader in, OutputWriter out) {
        int[] width = IOUtils.readIntArray(in, 7);
        long[][] matrices = new long[7][];
        for (int i = 1; i <= 7; i++) {
            long[][] matrix = new long[1 << i][1 << i];
            for (int j = 0; j < (1 << i); j++) {
                for (int k = 0; k < (1 << i); k++) {
                    for (int l = 0; l < (1 << (i - 1)); l++) {
                        int mask = 2 * l + 1 + (1 << i);
                        boolean good = true;
                        for (int m = 0; m < i; m++) {
                            if ((j >> m & 1) == 1 && (k >> m & 1) == 1 && (mask >> m & 1) == 1 && (mask >> (m + 1) & 1) == 1) {
                                good = false;
                                break;
                            }
                        }
                        if (good) {
                            matrix[j][k]++;
                        }
                    }
                }
            }
            matrices[i - 1] = Matrix.convert(matrix);
        }
        Matrix.mod = (long) (1e9 + 7);
        long[] result = new long[128];
        result[127] = 1;
        for (int i = 7; i >= 1; i--) {
            long[][] current = Matrix.convert(Matrix.power(matrices[i - 1], width[i - 1], Matrix.mod, 1 << i), 1 << i);
            long[] next = new long[result.length >> 1];
            for (int j = 0; j < next.length; j++) {
                for (int k = 0; k < result.length; k++) {
                    next[j] += current[j + next.length][k] * result[k] % Matrix.mod;
                }
                next[j] %= Matrix.mod;
            }
            result = next;
        }
        out.printLine(result[0]);
    }
}

class InputReader {

	private InputStream stream;
	private byte[] buf = new byte[1024];
	private int curChar;
	private int numChars;
	private SpaceCharFilter filter;

	public InputReader(InputStream stream) {
		this.stream = stream;
	}

	public int read() {
		if (numChars == -1)
			throw new InputMismatchException();
		if (curChar >= numChars) {
			curChar = 0;
			try {
				numChars = stream.read(buf);
			} catch (IOException e) {
				throw new InputMismatchException();
			}
			if (numChars <= 0)
				return -1;
		}
		return buf[curChar++];
	}

	public int readInt() {
		int c = read();
		while (isSpaceChar(c))
			c = read();
		int sgn = 1;
		if (c == '-') {
			sgn = -1;
			c = read();
		}
		int res = 0;
		do {
			if (c < '0' || c > '9')
				throw new InputMismatchException();
			res *= 10;
			res += c - '0';
			c = read();
		} while (!isSpaceChar(c));
		return res * sgn;
	}

	public boolean isSpaceChar(int c) {
		if (filter != null)
			return filter.isSpaceChar(c);
		return isWhitespace(c);
	}

	public static boolean isWhitespace(int c) {
		return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
	}

	public interface SpaceCharFilter {
		public boolean isSpaceChar(int ch);
	}
}

class OutputWriter {
	private final PrintWriter writer;

	public OutputWriter(OutputStream outputStream) {
		writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
	}

	public void close() {
		writer.close();
	}

	public void printLine(long i) {
		writer.println(i);
	}

}

class IOUtils {

	public static int[] readIntArray(InputReader in, int size) {
		int[] array = new int[size];
		for (int i = 0; i < size; i++)
			array[i] = in.readInt();
		return array;
	}

}

class Matrix {
	public static long mod = Long.MAX_VALUE;

	public static long[] convert(long[][] matrix) {
		long[] result = new long[matrix.length * matrix.length];
		for (int i = 0; i < matrix.length; i++) {
			for (int j = 0; j < matrix.length; j++)
				result[i * matrix.length + j] = matrix[i][j];
		}
		return result;
	}

	public static long[][] convert(long[] matrix, int side) {
		long[][] result = new long[side][side];
		for (int i = 0; i < side; i++) {
			for (int j = 0; j < side; j++)
				result[i][j] = matrix[i * side + j];
		}
		return result;
	}

	public static long[] power(long[] matrix, long exponent, long mod, int side) {
		long[] result = new long[matrix.length];
		long[] temp = new long[result.length];
		power(matrix, result, temp, exponent, mod, side);
		return result;
	}

	private static void power(long[] matrix, long[] result, long[] temp, long exponent, long mod, int side) {
		if (exponent == 0) {
			for (int i = 0; i < matrix.length; i += side + 1)
				result[i] = 1 % mod;
			return;
		}
		if ((exponent & 1) == 0) {
			power(matrix, temp, result, exponent >> 1, mod, side);
			multiply(result, temp, temp, mod, side);
		} else {
			power(matrix, temp, result, exponent - 1, mod, side);
			multiply(result, temp, matrix, mod, side);
		}
	}

	public static void multiply(long[] c, long[] a, long[] b, long mod, int side) {
		Arrays.fill(c, 0);
		for (int i = 0; i < side; i++) {
			for (int j = 0; j < side; j++) {
				for (int k = 0; k < side; k++) {
					c[i * side + k] += a[i * side + j] * b[j * side + k];
					if ((j & 3) == 3) {
						c[i * side + k] %= mod;
					}
				}
			}
		}
		for (int i = 0; i < c.length; i++)
			c[i] %= mod;
	}

}