Skewness

题号：NC52854
时间限制：C/C++/Rust/Pascal 5秒，其他语言10秒
空间限制：C/C++/Rust/Pascal 32 M，其他语言64 M
Special Judge, 64bit IO Format: %lld

题目描述

Bobo has a matrix A with n rows and n columns.
For submatrix with upper-left corner $(x_1, y_1)$ and lower-right corner $(x_2, y_2)$ ( $1 \leq x_1 \leq x_2 \leq n, 1 \leq y_1 \leq y_2 \leq n$ ),
he defined its *skewness* $S(x_1, y_1, x_2, y_2) = \left(\sum_{i = x_1}^{x_2} \sum_{j = y_1}^{y_2} A_{i, j}\right)^3$ .
Bobo would like to know the sum of *skewness* of all submatrices modulo $(10^9+7)$ .

输入描述:

The input contains zero or more test cases and is terminated by end-of-file. For each test case:
The first line contains an integer n.
The i-th of following n lines contains n integers .

* 
* 
* The number of test cases does not exceed 10.

输出描述:

For each case, output an integer which denotes the sum.

示例1

输入

复制

输出

复制

14
448