Coin Rows solution codeforces

Coin Rows solution codeforces


Alice and Bob are playing a game on a matrix, consisting of 22 rows and mm columns. The cell in the ii-th row in the jj-th column contains ai,jai,j coins in it.

Initially, both Alice and Bob are standing in a cell (1,1)(1,1). They are going to perform a sequence of moves to reach a cell (2,m)(2,m).

The possible moves are:

  • Move right — from some cell (x,y)(x,y) to (x,y+1)(x,y+1);
  • Move down — from some cell (x,y)(x,y) to (x+1,y)(x+1,y).

First, Alice makes all her moves until she reaches (2,m)(2,m). She collects the coins in all cells she visit (including the starting cell).

When Alice finishes, Bob starts his journey. He also performs the moves to reach (2,m)(2,m) and collects the coins in all cells that he visited, but Alice didn’t.

The score of the game is the total number of coins Bob collects.

Alice wants to minimize the score. Bob wants to maximize the score. What will the score of the game be if both players play optimally?

Input

The first line contains a single integer tt (1t1041≤t≤104) — the number of testcases.

Then the descriptions of tt testcases follow.

The first line of the testcase contains a single integer mm (1m1051≤m≤105) — the number of columns of the matrix.

The ii-th of the next 22 lines contain mm integers ai,1,ai,2,,ai,mai,1,ai,2,…,ai,m (1ai,j1041≤ai,j≤104) — the number of coins in the cell in the ii-th row in the jj-th column of the matrix.

The sum of mm over all testcases doesn’t exceed 105105.

Output

For each testcase print a single integer — the score of the game if both players play optimally.

Example

input

Copy
3
3
1 3 7
3 5 1
3
1 3 9
3 5 1
1
4
7

output

Copy
7
8
0
Note

The paths for the testcases are shown on the following pictures. Alice’s path is depicted in red and Bob’s path is depicted in blue.

Coin Rows solution codeforces

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