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;
bool is_prime(int n) {
  for (int i = 2; i * i <= n; ++i) {
    if (n % i == 0) {
      return false;
    }
  }
  return true;
}
inline long long getPow(long long a, long long b) {
  long long res = 1, tp = a;
  while (b) {
    if (b & 1ll) {
      res *= tp;
      res %= 1000000007;
    }
    tp *= tp;
    tp %= 1000000007;
    b >>= 1ll;
  }
  return res;
}
inline long long to_ll(string s) {
  long long cur = 0;
  for (int i = 0; i < s.size(); i++) {
    cur = cur * 10 + s[i] - '0';
  }
  return cur;
}
inline string to_str(long long x) {
  string s = "";
  while (x) {
    s += char(x % 10 + '0');
    x /= 10;
  }
  reverse(s.begin(), s.end());
  return s;
}
inline long long nxt() {
  long long x;
  scanf("%lld", &x);
  return x;
}
void ok() {
  puts("YES");
  exit(0);
}
void panic() {
  puts("NO");
  exit(0);
}
const long long N = 1e6 + 5;
int main() {
  long long n = nxt();
  vector<long long> mas(n);
  for (int i = 0; i < n; i++) {
    mas[i] = nxt();
  }
  long long m = n;
  while (m--) {
    bool f = 1;
    for (int i = 0; i < n; i++) {
      if (mas[i] != i) {
        f = 0;
      }
    }
    if (f) {
      ok();
    }
    for (int i = 0; i < n; i++) {
      if (i % 2) {
        mas[i]--;
        mas[i] += n;
        mas[i] %= n;
      } else {
        mas[i]++;
        mas[i] %= n;
      }
    }
  }
  panic();
  return 0;
}
