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.