Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ACM-ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

E. Stairs and Lines

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

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

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

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 *w*_{1}, *w*_{2}, ..., *w*_{7} (0 ≤ *w*_{i} ≤ 10^{5}). It is guaranteed that at least one of the *w*_{i}'s isn't equal to zero.

Output

In the single line of the output display a single number — the answer to the problem modulo 10^{9} + 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:

Codeforces (c) Copyright 2010-2017 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: May/25/2017 02:27:07 (p1).

Desktop version, switch to mobile version.
User lists

Name |
---|