Andrewid the Android is a galaxy-famous detective. He is now investigating a case of frauds who make fake copies of the famous Stolp's gears, puzzles that are as famous as the Rubik's cube once was.

Its most important components are a button and a line of n similar gears. Each gear has n teeth containing all numbers from 0 to n - 1 in the counter-clockwise order. When you push a button, the first gear rotates clockwise, then the second gear rotates counter-clockwise, the the third gear rotates clockwise an so on.

Besides, each gear has exactly one active tooth. When a gear turns, a new active tooth is the one following after the current active tooth according to the direction of the rotation. For example, if n = 5, and the active tooth is the one containing number 0, then clockwise rotation makes the tooth with number 1 active, or the counter-clockwise rotating makes the tooth number 4 active.

Andrewid remembers that the real puzzle has the following property: you can push the button multiple times in such a way that in the end the numbers on the active teeth of the gears from first to last form sequence 0, 1, 2, ..., n - 1. Write a program that determines whether the given puzzle is real or fake.

Input

The first line contains integer n (1 ≤ n ≤ 1000) — the number of gears.

The second line contains n digits a1, a2, ..., an (0 ≤ ai ≤ n - 1) — the sequence of active teeth: the active tooth of the i-th gear contains number ai.

Output

In a single line print "Yes" (without the quotes), if the given Stolp's gears puzzle is real, and "No" (without the quotes) otherwise.

Examples

Input

3
1 0 0


Output

Yes


Input

5
4 2 1 4 3


Output

Yes


Input

4
0 2 3 1


Output

No

Note

In the first sample test when you push the button for the first time, the sequence of active teeth will be 2 2 1, when you push it for the second time, you get 0 1 2.
#include <bits/stdc++.h>
using namespace std;
int n;
bool solve(string &s) {
  if (s == "" || s.length() <= 1) return false;
  for (int i = 0; i < n - 1; i++) {
    if (s[i] - '0' + s[i + 1] - '0' == 1) {
      s = s.substr(0, i) + s.substr(i + 2, n);
      return true;
    }
  }
  return false;
}
int main() {
  ios_base::sync_with_stdio(false);
  int n;
  cin >> n;
  int a[n], b[n];
  for (int i = (0); i < (n); ++i) {
    cin >> a[i];
    b[i] = a[i];
  }
  bool val = true;
  while (1) {
    val = true;
    for (int i = (0); i < (n); ++i) {
      if (i & 1) {
        if (a[i] == 0)
          a[i] = n - 1;
        else
          a[i] = (a[i] - 1) % n;
      } else
        a[i] = (a[i] + 1) % n;
    }
    for (int i = (0); i < (n); ++i)
      if (a[i] != i) {
        val = false;
        break;
      }
    if (val) break;
    int c = 0;
    for (int i = (0); i < (n); ++i) {
      if (a[i] == b[i])
        c++;
      else
        break;
    }
    if (c == n) {
      val = false;
      break;
    }
  }
  if (val)
    cout << "Yes";
  else
    cout << "No";
  return 0;
}
