Perfect Number with Divisor Pairs

Source: Phước Hưng OJ

Version: Phuoc Hung OJ Extended

Problem Statement

A positive integer n is perfect if the sum of all its positive proper divisors equals n. Determine whether n is perfect.

Input

One positive integer n.

Output

Print YES if perfect, otherwise NO.

Subtasks

• Subtask 1 (20%): 1≤n≤100.
• Subtask 2 (30%): 1≤n≤100000.
• Subtask 3 (50%): 1≤n≤100000000.

Examples

Example 1

Input

6

Output

YES

Explanation

Proper divisors 1,2,3 sum to six.

Example 2

Input

1

Output

NO

Explanation

One has no proper positive divisors.