Vasya and Petya wrote down all integers from 1 to n to play the "powers" game (n can be quite large; however, Vasya and Petya are not confused by this fact).

Players choose numbers in turn (Vasya chooses first). If some number x is chosen at the current turn, it is forbidden to choose x or all of its other positive integer powers (that is, x^2, x^3, ...) at the next turns. For instance, if the number 9 is chosen at the first turn, one cannot choose 9 or 81 later, while it is still allowed to choose 3 or 27. The one who cannot make a move loses.

Who wins if both Vasya and Petya play optimally?


-----Input-----

Input contains single integer n (1 ≤ n ≤ 10^9).


-----Output-----

Print the name of the winner — "Vasya" or "Petya" (without quotes).


-----Examples-----
Input
1

Output
Vasya

Input
2

Output
Petya

Input
8

Output
Petya



-----Note-----

In the first sample Vasya will choose 1 and win immediately.

In the second sample no matter which number Vasya chooses during his first turn, Petya can choose the remaining number and win.

Difficulty: competition

Starter code:

Solutions:
from sys import stdin, stdout
import math, collections
mod = 10**9+7

def isPower(n):
    if (n <= 1):
        return True
    for x in range(2, (int)(math.sqrt(n)) + 1):
        p = x
        while (p <= n):
            p = p * x
            if (p == n):
                return True

    return False
n = int(input())
arr = [0,1,2,1,4,3,2,1,5,6,2,1,8,7,5,9,8,7,3,4,7,4,2,1,10,9,3,6,11,12]
ans = arr[int(math.log(n, 2))]
s = int(math.log(n, 2))
for i in range(3, int(n**0.5)+1):
    if not isPower(i):
        ans^=arr[int(math.log(n, i))]
        s+=int(math.log(n, i))
ans^=((n-s)%2)
print("Vasya" if ans else "Petya")

import math, collections
mod = 10**9+7

def isPower(n):
    if (n <= 1):
        return True
    for x in range(2, (int)(math.sqrt(n)) + 1):
        p = x
        while (p <= n):
            p = p * x
            if (p == n):
                return True
    return False
n = int(input())
arr = [0,1,2,1,4,3,2,1,5,6,2,1,8,7,5,9,8,7,3,4,7,4,2,1,10,9,3,6,11,12]
ans = arr[int(math.log(n, 2))]
s = int(math.log(n, 2))
for i in range(3, int(n**0.5)+1):
    if not isPower(i):
        ans^=arr[int(math.log(n, i))]
        s+=int(math.log(n, i))
ans^=((n-s)%2)
print("Vasya" if ans else "Petya")