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.
#include <bits/stdc++.h>
const int MAXN = 1e6 + 5;
int n;
int a[MAXN];
struct BIT {
  int a[MAXN];
  void init() { memset(a, 0, sizeof(a)); }
  int lb(int x) { return x & -x; }
  void modify(int pos, int val) {
    for (int i = pos; i <= n; i += lb(i)) a[i] += val;
  }
  int query(int pos) {
    int res = 0;
    for (int i = pos; i > 0; i -= lb(i)) res += a[i];
    return res;
  }
  int query(int l, int r) { return query(r) - query(l - 1); }
} bit;
int main() {
  scanf("%d", &n);
  for (int i = 1; i <= n; i++) scanf("%d", &a[i]);
  int rev = 0;
  for (int i = 1; i <= n; i++) {
    rev += bit.query(a[i] + 1, n);
    bit.modify(a[i], 1);
  }
  if ((rev & 1) == ((n * 3) & 1)) puts("Petr");
  if ((rev & 1) == ((n * 7 + 1) & 1)) puts("Um_nik");
  return 0;
}
