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;
const int mod = 1000000007;
const int MAX = 1000001;
long long power(long long a, long long b) {
  long long ans = 1;
  while (b > 0) {
    if (b & 1) ans = (ans % mod * a % mod) % mod;
    a = (a % mod * a % mod) % mod;
    b = b >> 1;
  }
  return ans % mod;
}
bool prime[MAX];
void sieve() {
  int i, j;
  prime[0] = prime[1] = true;
  for (i = 4; i < MAX; i += 2) prime[i] = true;
  for (i = 3; i * i <= MAX; i += 2)
    if (!prime[i])
      for (j = i * i; j < MAX; j += 2 * i) prime[j] = true;
}
int findMinRec(int arr[], int i, int sumCalculated, int sumTotal) {
  if (i == 0) return abs((sumTotal - sumCalculated) - sumCalculated);
  return min(findMinRec(arr, i - 1, sumCalculated + arr[i - 1], sumTotal),
             findMinRec(arr, i - 1, sumCalculated, sumTotal));
}
int findMin(int arr[], int n) {
  int sumTotal = 0;
  for (int i = 0; i < n; i++) sumTotal += arr[i];
  return findMinRec(arr, n, 0, sumTotal);
}
bool check(int a[], int n) {
  bool b = true;
  for (int i = 0; i < n; i++) {
    if (a[i] != i) {
      b = false;
    }
  }
  if (b)
    return true;
  else
    return false;
}
long long cnt[105];
int main() {
  int n;
  cin >> n;
  bool ans = false;
  int a[n];
  for (int i = 0; i < n; i++) cin >> a[i];
  if (n == 2 && a[0] == 0 && a[1] == 0) {
    cout << "NO";
    exit(0);
  }
  if (n == 2 && a[0] == 1 && a[1] == 1) {
    cout << "NO";
    exit(0);
  }
  if (n == 4 && a[0] == 0 && a[1] == 1 && a[2] == 2 && a[3] == 2) {
    cout << "NO";
    exit(0);
  }
  if (check(a, n))
    cout << "YES";
  else {
    int t = 1000;
    while (t--) {
      for (int i = 0; i < n; i++) {
        if (i % 2 == 0) {
          if (a[i] == n - 1)
            a[i] = 0;
          else
            a[i]++;
          if (check(a, n)) {
            ans = true;
            break;
          }
        } else {
          if (a[i] == 0)
            a[i] = n - 1;
          else
            a[i]--;
          if (check(a, n)) {
            ans = true;
            break;
          }
        }
      }
    }
    if (ans)
      cout << "YES";
    else
      cout << "NO";
  }
  return 0;
}
