#85 Array and Counting 2

Statement

Statement language

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.

Input

The input is given in the following format.

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

Output

Print the answer of the problem on the first line.

Constraints

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

Subtasks

#	Score	Constraints
1	14	$N \leq 200$ .
2	27	$N \leq 2 \ 000$ .
3	59	No additional constraints.

Samples

Sample 1

Input

5
1 2 3 4 5

Output

9

Sample 2

Input

4
1 1 1 1

Output

10