A positive integer $N$ and a sequence $A = [A_1, A_2, \cdots, A_{N}]$ of length $N$ are given. Find the number of integer pairs $(l, r)$ that satisfy the following conditions.

• $1 \leq l \leq r \leq N$.
• The arithmetic mean of the subarray $[A_l, A_{l + 1}, \cdots, A_r]$ is an integer.

The input is given in the following format.

$N$ $A_1 \ A_2 \ \cdots \ A_{N}$

Print the answer of the problem on the first line.

• $1 \leq N \leq 200 \ 000$.
• $1 \leq A_i \leq 100$ ($1 \leq i \leq N$).