Kyriakos Grizzly is once again hosting a party in celebration of finally hitting a OAC (one-arm chin-up)! To celebrate he has lined up $N$ platters of food with the $i^{\text{th}}$ platter containing $a_i$ servings of delicious protein! To host a party Kyriakos will first choose a continuous subsection of platters of length $K$ and invite $K$ of his friends to help him finish the food. Of course since everyone loves protein, Kyriakos will only consider choosing a party with $K$ people if and only if the total number of servings of protein can be split equally among all the $K$ partygoers. This way no one can complain that another person ate more protein than them. Help Kyriakos determine how many different parties he can host!

Constraints

$1\le N\le {10}^5$

$1\le a_i\le 100$

Subtask 1 [30%]

$1\le a_i\le 2$

Subtask 2 [70%]

No additional constraints.

Input Specification

The first line of input will consist of a single integer $N$. The second and final line of input will contain $N$ spaced out integers with the $i^{\text{th}}$ one denoting the number of servings of protein on the $i^{\text{th}}$ platter.

Output Specification

Output a single integer, the number of different parties Kyriakos can choose from.

Sample Input

4
6 9 4 20

Sample Output

6

Explanation

The valid parties that Kyriakos can choose are $[9,4,20]$, $[6]$, $[9]$, $[4]$, $[20]$, and $[4,20]$. There are $6$ possibilities.