Petr likes to come up with problems about randomly generated data. This time problem is about random permutation. He decided to generate a random permutation this way: he takes identity permutation of numbers from 1 to n and then 3n times takes a random pair of different elements and swaps them. Alex envies Petr and tries to imitate him in all kind of things. Alex has also come up with a problem about random permutation. He generates a random permutation just like Petr but swaps elements 7n+1 times instead of 3n times. Because it is more random, OK?!

You somehow get a test from one of these problems and now you want to know from which one.

Input

In the first line of input there is one integer n (10^{3} ≤ n ≤ 10^{6}).

In the second line there are n distinct integers between 1 and n — the permutation of size n from the test.

It is guaranteed that all tests except for sample are generated this way: First we choose n — the size of the permutation. Then we randomly choose a method to generate a permutation — the one of Petr or the one of Alex. Then we generate a permutation using chosen method.

Output

If the test is generated via Petr's method print "Petr" (without quotes). If the test is generated via Alex's method print "Um_nik" (without quotes).

Example

Input

5
2 4 5 1 3


Output

Petr

Note

Please note that the sample is not a valid test (because of limitations for n) and is given only to illustrate input/output format. Your program still has to print correct answer to this test to get AC.

Due to randomness of input hacks in this problem are forbidden.
import java.util.*;

public class B {
	static int[] ar = new int[2000006];
	static int[] dp = new int[20000005];

	public static int rec(int val) {
		if (dp[val] > 0)
			return 0;
		dp[val] = 1;
		return 1 + rec(ar[val]);
	}

	public static void main(String[] args) {
		Scanner t = new Scanner(System.in);
		int n = t.nextInt();
		for (int i = 1; i <= n; i++) {
			ar[i] = t.nextInt();
		}
		int ret=0;
		for(int i=1;i<=n;i++) {
			if(dp[i]==0) {
				ret+=rec(ar[i]);
				ret--;
			}
		}
		
		if(ret%2==n%2)
		System.out.println("Petr");
		else System.out.println("Um_nik");
	}
}