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>
template <typename T>
using Vector2D = std::vector<std::vector<T>>;
template <typename T>
using Vector3D = std::vector<Vector2D<T>>;
using PairInt = std::pair<int, int>;
using PairInt64 = std::pair<int64_t, int64_t>;
using MapInt = std::map<int, int>;
using UMapIntString = std::unordered_map<int, std::string>;
using SetInt = std::set<int>;
using SetPairInt64 = std::set<PairInt64>;
using VectorInt = std::vector<int>;
using VectorInt2D = Vector2D<int>;
using VectorInt64 = std::vector<int64_t>;
using VectorInt642D = Vector2D<int64_t>;
using VectorChar = std::vector<char>;
using VectorChar2D = Vector2D<char>;
using VectorString = std::vector<std::string>;
using QueuePairInt = std::queue<PairInt>;
using QueueInt = std::queue<int>;
using VectorPairInt = std::vector<PairInt>;
using VectorPairInt2D = Vector2D<PairInt>;
using SetInt = std::set<int>;
using UMapChar = std::map<char, int>;
using ListInt = std::list<int>;
using VectorListInt = std::vector<ListInt>;
using VectorDouble = std::vector<double>;
int main() {
  std::ios::sync_with_stdio(false);
  int n;
  std::cin >> n;
  VectorInt wheels(n);
  for (int i = 0; i < n; ++i) {
    std::cin >> wheels[i];
  }
  int k = n - wheels[0];
  bool ans = true;
  for (int i = 0; ans && i < n; ++i) {
    if (i % 2 == 0) {
      ans = ans && ((wheels[i] + k) % n == i);
    } else {
      int v = wheels[i] - k;
      if (v < 0) {
        v = n + v;
      }
      ans = ans && (v == i);
    }
  }
  std::cout << (ans ? "YES" : "NO");
  return 0;
}
