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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.Arrays;

public class C485E {
    public static void main(String[] args) throws NumberFormatException, IOException {
            
            BufferedReader sc = new BufferedReader(new InputStreamReader(System.in));
            
            int n = Integer.parseInt(sc.readLine());
            String[] t = sc.readLine().split(" ");
            int[] list = new int[n];
            for(int x=0; x<n; x++){
                list[x] = Integer.parseInt(t[x]);
            }
            
            boolean even = false;
            if(list.length % 2 ==1) {
                even = true;
            }
            
            boolean ans = invCount(list);
            
            //System.out.println(even +" "+ ans);
            
            if(even ^ ans) {
                System.out.print("Petr");
            }
            else {
                System.out.print("Um_nik");
            }
    }
    
    static boolean merge(int[] arr, int[] left, int[] right) {
        int i = 0, j = 0;
        boolean count = true;
        while (i < left.length || j < right.length) {
            if (i == left.length) {
                arr[i+j] = right[j];
                j++;
            } else if (j == right.length) {
                arr[i+j] = left[i];
                i++;
            } else if (left[i] <= right[j]) {
                arr[i+j] = left[i];
                i++;                
            } else {
                arr[i+j] = right[j];
                count ^= (left.length-i)%2==1;
                j++;
            }
        }
        return count;
    }

    static boolean invCount(int[] arr) {
        if (arr.length < 2)
            return true;

        int m = (arr.length + 1) / 2;
        int left[] = Arrays.copyOfRange(arr, 0, m);
        int right[] = Arrays.copyOfRange(arr, m, arr.length);

        return invCount(left) ^ invCount(right) ^ merge(arr, left, right);
    }
}
