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Arithmetic Slices 1

1. You are given an array(arr) of integers. 2. You have to find the count of arithmetic slices in the given array. 3. Arithmetic slice is defined as the sub-array having all its elements in A.P and the length of sub-array should be greater than or equal to 3.

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Arithmetic Slices 1

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1. You are given an array(arr) of integers. 2. You have to find the count of arithmetic slices in the given array. 3. Arithmetic slice is defined as the sub-array having all its elements in A.P and the length of sub-array should be greater than or equal to 3.

Constraints

1 <= N <= 10^8 -10^8 <= arr[i] <= 10^8

Format

Input

A number N arr1 arr2.. N numbers

Output

Check the sample output and question video.

Example

Sample Input

4 1 2 3 4

Sample Output

3

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