Subarray GCD

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Points: 7 (partial)
Time limit: 2.0s
Memory limit: 128M

Problem types

Given an array A of length N, count the number of distinct greatest common divisors (GCDs) of all subarrays of this array.

We define the greatest common divisor of a subarray as the greatest common divisor of all the subarray's elements.

Input Specification

The first line of input will contain the integer N\ (1 \leq N \leq 10^5), the length of the array A.

The next line will contain N space separated integers A_i\ (1 \leq A_i \leq 10^9)

Output Specification

One line, the number of distinct subarray GCDs.


Subtask 1 [30%]

N \leq 10^3

Subtask 2 [70%]

No further restrictions.

Sample Input

1 6 4

Sample Output



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