Good array (perfect)

Description

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Smart likes to use arrays. Today, he needs your help to complete a difficult task.
If for each non-empty sub-array of the array \(A\) (a sub-array is an array consisting of several consecutive elements selected from the value \(A\)), if the sum of all the elements of the sub-array is not equal to zero, it is called "Perfect Array". For example, the array \(\{−1,2,−3\}\) is "Perfect Array" because all its sub-arrays \(\{−1\}\), \(\{− 1, 2\}\) , \(\{− 1, 2, -3\}\), \(\{2\}\), \(\{2, -3\}\), and the sum of the elements of \(\{-3\}\) are all non-zero. However, the array \(\{−1, 2, −1, −3\}\) is not "Perfect Array" because the elements of its subarray \(\{−1, 2, −1\}\) The sum is equal to 0.
Your task is to help Smart calculate the number of "Perfect Array" in the non-empty sub-array of \(A\) for a given array \(A\).

Format

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Input

The first line contains an integer \(n\), which represents the length of the array \(A\).
The second line contains \(n\) integers \(A_1, A_2, \cdots, A_n\) for the elements of the array \(A\).

Output

Only one line of the output contains an integer, indicating that the non-empty sub-array of the array \(A\) is the number of "Perfect Array".

Sample

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Input

3
1 2 -3

Output

5

Sample Explanation

Sub-array \(\{−1\}\) of array \(\{1, 2, -3\}\), \(\{− 1, 2\}\), \(\{− 1, 2, -3\}\), \(\{2\}\), \(\{2, -3\}\), \(\{-3\}\) is "Perfect Array", but the sub-array \(\{1, 2, −3\}\) is not "Perfect Array".

Hint

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\(50\%\) data: \(n \le 1000\);
Data for \(100\%\): \(1 \le n \le 2 \times 10^5\), \(-10^9 \le A_i \le 10^9\).

Sample Code

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Code is not available!