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.Scanner;

public class CF987E {
	static long total;
	static int[] arr;
	
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		arr = new int[n];
		for(int i=0; i<n; i++) arr[i] = sc.nextInt();
		mergeSort(0, n-1);
		if(n%2==0) System.out.println(total%2==0 ? "Petr" : "Um_nik");
		else System.out.println(total%2==1 ? "Petr" : "Um_nik");
	}
	
	private static void mergeSort(int l, int r) {
		if(l<r) {
			int m = (l+r)/2;
			mergeSort(l, m);
			mergeSort(m+1, r);
			merge(l, m, r);
		}
	}

	private static void merge(int l, int m, int r) {
		int n1 = m - l + 1;
        int n2 = r - m;
        int L[] = new int [n1];
        int R[] = new int [n2];
        for (int i=0; i<n1; i++) L[i] = arr[l + i];
        for (int j=0; j<n2; j++) R[j] = arr[m + 1+ j];
        int i = 0, j = 0;
        int k = l;
        while (i < n1 && j < n2) {
            if (L[i] <= R[j]) arr[k++] = L[i++];
            else {
            	arr[k++] = R[j++];
            	total += n1-i;
            }
        }
        while (i < n1) arr[k++] = L[i++];
        while (j < n2) arr[k++] = R[j++];
	}
}
