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;
char __INPUT[25];
inline int _Int() {
  scanf("%s", __INPUT);
  return atoi(__INPUT);
}
inline long long int _LLi() {
  scanf("%s", __INPUT);
  return atoll(__INPUT);
}
long long int bigMod(long long int A, long long int P, int M) {
  long long int R = 1;
  for (A %= M; P; P >>= 1) {
    if (P & 1) R = (R * A) % M;
    A = (A * A) % M;
  }
  return R;
}
long long int bigMul(long long int A, long long int B, long long int M) {
  long long int R = 0;
  for (A %= M; B; B >>= 1) {
    if (B & 1) R = (R + A) % M;
    A = (A + A) % M;
  }
  return R;
}
unsigned long long int _pow(unsigned long long int A, int P) {
  unsigned long long int R = 1;
  for (; P; P >>= 1) {
    if (P & 1) R = (R * A);
    A = (A * A);
  }
  return R;
}
template <class T>
T GCD(T x, T y) {
  while (x) x ^= y ^= x ^= y %= x;
  return y;
}
int x[10001];
void Main() {
  int n = _Int();
  for (int i = 0; i < n; i++) x[i] = _Int();
  for (; x[0];) {
    for (int i = 0; i < n; i++) {
      if (i & 1)
        x[i]++;
      else
        x[i]--;
      if (x[i] == -1) x[i] = n - 1;
      if (x[i] == n) x[i] = 0;
    }
  }
  for (int i = 0; i < n; i++) {
    if (x[i] != i) {
      printf("No");
      return;
    }
  }
  printf("Yes");
}
int main() {
  Main();
  return 0;
}
