Light, more light

Source: UVa

Version: Phuoc Hung OJ Extended

Problem Statement

There are $n$ light bulbs numbered from $1$ to $n$. Initially, every bulb is off.

Exactly $n$ passes are performed. On pass $i$, the state of every bulb whose number is divisible by $i$ is toggled.

Determine the final state of bulb $n$.

Input

One positive integer $n$.

Output

Print yes if bulb $n$ is on after all passes; otherwise print no.

Subtasks

• Subtask 1 (20%): $n\le10^4$.
• Subtask 2 (30%): $n\le10^9$.
• Subtask 3 (50%): Full constraints: $1\le n\le2^{32}-1$.

Examples

Input

4

Output

yes

Explanation

Initially all four bulbs are off. Track bulb $4$ through the four passes:

• Pass $1$: bulb $4$ changes from off to on.
• Pass $2$: bulb $4$ changes from on to off.
• Pass $3$: bulb $4$ is not affected, so it remains off.
• Pass $4$: bulb $4$ changes from off to on.

After the final pass, bulb $4$ is on, so the program prints yes.