CF498E.Stairs and Lines

You 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.

给你一个网格上的图形，该图形表示一个由 7 级台阶组成的楼梯。第 $i$ 级台阶的宽度为 $w_i$ 个方格。形式上，该图形是通过依次拼接尺寸为 $w_i \times i$ 的矩形而构造的，且所有矩形的边长为 $w_i$ 的边均位于同一条直线上。例如，若所有 $w_i = 1$，则该图形如下图所示（不同颜色代表不同的矩形）：

而当 $w = \{5,\,1,\,0,\,3,\,0,\,0,\,1\}$ 时，其图形如下所示：

请计算对图形中各内部方格的某些边进行染色的方法数，使得任意一个方格的四条边均不被全部染色。图形外轮廓上的方格边默认已被染色。考虑图形旋转后得到的不同染色方案视为不同的方案。

The single line of the input contains 7 numbers _w_1, _w_2, ..., _w_7 (0 ≤ w__i ≤ 105). It is guaranteed that at least one of the w__i's isn't equal to zero.

输入仅有一行，包含 7 个数字 $w_1,\,w_2,\,\dots,\,w_7$（$0\le w_i\le 10^5$）。保证至少有一个 $w_i$ 不等于零。

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

在输出的单行中显示一个数字——问题答案对 $10^9 + 7$ 取模的结果。

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

第三组样例的所有可能涂色方式如下所示：