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.
//package codeforcesround.year2015.june.round310;

import java.io.BufferedReader;
import java.io.FileInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.StringTokenizer;
 
public class FakeNumbers {
        InputReader in;
        PrintWriter out;
        boolean submit;
        
        private void debug(Object... o) {
                if(!submit) {
                        System.out.println(Arrays.deepToString(o));
                }
        }
 
        public static void main(String args[]) throws IOException {
                new FakeNumbers();
        }
        
        public FakeNumbers() throws IOException {
                long start = System.currentTimeMillis();
                submit = !false;
                if(submit == false) in = new InputReader(new FileInputStream("D:\\input.txt"));
                else in = new InputReader(System.in);
                out = new PrintWriter(System.out);
                
                int t = 1;
                while(t-- > 0)
                        solve();
                
                long end = System.currentTimeMillis();
                debug(end - start, " ms");
                out.close();
        }
        
        private void solve() throws IOException {
                int N = in.nextInteger();
                int A[] = new int[N];
                for(int i = 0; i < N; i++) {
                        A[i] = in.nextInteger();
                }
                int diff = N - A[0];
                for(int i = 0; i < N; i++) {
                        if(i % 2 == 0) {
                                A[i] = (A[i] + diff) % N;
                        } else {
                                A[i] = (A[i] - diff) % N;
                                if(A[i] < 0) {
                                        A[i] += N;
                                }
                        }
                }
                boolean fake = false;
                for(int i = 0; i < N; i++) {
                        if(A[i] != i) {
                                fake = true;
                                break;
                        }
                }
                if(fake) {
                        out.println("No");
                } else {
                        out.println("Yes");
                }
        }

        static class InputReader {
                public BufferedReader reader;
                public StringTokenizer tokenizer;

                public InputReader(InputStream stream) {
                        reader = new BufferedReader(new InputStreamReader(stream));
                        tokenizer = null;
                }

                public String next() {
                        while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                                try {
                                        tokenizer = new StringTokenizer(reader.readLine());
                                } catch (IOException e) {
                                        throw new RuntimeException(e);
                                }
                        }
                        return tokenizer.nextToken();
                }

                public String nextString() {
                        return next();
                }

                public int nextInteger() {
                        return Integer.parseInt(next());
                }

                public long nextLong() {
                        return Long.parseLong(next());
                }

                public float nextFloat() {
                        return Float.parseFloat(next());
                }

                public double nextDouble() {
                        return Double.parseDouble(next());
                }
        }
}