Prime Check with While

Source: Phước Hưng OJ

Version: Phuoc Hung OJ Extended

Problem Statement

Given integer n, determine whether it is prime. A prime is an integer greater than one with exactly two positive divisors, 1 and itself.

Input

One integer n.

Output

Print YES if n is prime, otherwise NO.

Subtasks

• Subtask 1 (20%): 0 ≤ n ≤ 50.
• Subtask 2 (30%): 0 ≤ n ≤ 100000.
• Subtask 3 (50%): 0 ≤ n ≤ 1000000000.

Examples

Example 1

Input

1

Output

NO

Explanation

One has fewer than two positive divisors.

Example 2

Input

29

Output

YES

Explanation

No candidate divisor 2 through 5 divides 29.