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;
inline int toInt(string s) {
  int v;
  istringstream sin(s);
  sin >> v;
  return v;
}
inline long long toll(string s) {
  long long v;
  istringstream sin(s);
  sin >> v;
  return v;
}
template <class T>
inline string toString(T x) {
  ostringstream sout;
  sout << x;
  return sout.str();
}
vector<int> dfs_num;
vector<vector<int> > g;
vector<int> color;
vector<int> indegree;
vector<int> ts;
vector<int> num;
int n;
bool isCorrect() {
  bool flag = true;
  for (int i = 0; i < num.size(); i++) {
    if (num[i] != i) {
      flag = false;
    }
    if (i % 2 == 0) {
      num[i] = (num[i] + 1) % n;
    } else {
      num[i]--;
      if (num[i] < 0) {
        num[i] = n - 1;
      }
    }
  }
  return flag;
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  num.clear();
  cin >> n;
  for (int i = 0; i < n; i++) {
    int x;
    cin >> x;
    num.push_back(x);
  }
  if (n == 1 && num[0] == 0) {
    cout << "Yes" << endl;
    return 0;
  }
  for (int i = 0; i < n; i++) {
    if (isCorrect()) {
      cout << "Yes" << endl;
      return 0;
    }
  }
  cout << "No" << endl;
  return 0;
}
