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.io.*;
import java.util.*;
import java.math.*;

public class Test77 {

    static int[] n;

    public static void main(String[] z) throws Exception{
        Scanner s = new Scanner(System.in);
        int a = s.nextInt(), petr = a*3, lesha = a*7+1, o=0, i=0, h=0;
        int[] m = new int[a], k = new int[a];
        n = new int[a];
        for(int q=0; q<a; q++) {m[q] = s.nextInt(); k[q] = m[q]; n[q] = q+1;}
        PyraSort.sort(k);
        for(int q=0; q<a; q++){
            if(m[q]==q+1) o+=0;
            else{
                o+=1;
                i = m[q];
                m[q] = q+1;
                m[n[q]-1] = i;
                n[i-1] ^= n[q] ^= n[i-1];
                n[q] ^= n[i-1];
            }
        }
        System.out.println(o%2==petr%2 ? "Petr" : "Um_nik");
    }

    static class PyraSort {

        private static int heapSize;

        public static void sort(int[] a) {
            buildHeap(a);
            while (heapSize > 1) {
                swap(a, 0, heapSize - 1);
                heapSize--;
                heapify(a, 0);
            }
        }

        private static void buildHeap(int[] a) {
            heapSize = a.length;
            for (int i = a.length / 2; i >= 0; i--) {
                heapify(a, i);
            }
        }

        private static void heapify(int[] a, int i) {
            int l = 2 * i + 2;
            int r = 2 * i + 1;
            int largest = i;
            if (l < heapSize && a[i] < a[l]) {
                largest = l;
            }
            if (r < heapSize && a[largest] < a[r]) {
                largest = r;
            }
            if (i != largest) {
                swap(a, i, largest);
                heapify(a, largest);
            }
        }

        private static void swap(int[] a, int i, int j) {
            a[i] ^= a[j] ^= a[i];
            a[j] ^= a[i];
            n[i]^=n[j]^=n[i];
            n[j] ^= n[i];
        }
    }
}