## 07 Jul Friday Evening Python Homework 07.05.

**Question:**

Troy loves triangles. He especially likes counting triangles. He has an N-by-N grid consisting of either “.” or “#” characters. Help him count the number of triangles formed only by “#” characters in the grid. Triangles are of the form

More formally, a triangle of height h consists of h rows for some positive integer h. The ith row contains 2i − 1 “#” characters for i = 1, . . . , h. The rows are centred above each other so that they are symmetrical about a vertical line down their middle.

**Input Specification**

The first line contains the number N (1 ≤ N ≤ 2000) representing the size of the grid. The next N lines each contain N characters as described above.

**Output Specification**

Output the number of triangles in the grid.

**Sample Input**

**Explanation of Output for Sample Input**

There are 11 triangles of height one, 4 triangles of height two and 1 triangle of height three.

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