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 R310;
import java.io.IOException;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.InputMismatchException;
import java.util.Scanner;

public class q2 {
    public static void main(String[] args) {
        FasterScanner s = new FasterScanner();
        PrintWriter out=new PrintWriter(System.out);
        int n=s.nextInt(),a1=0,a2=0;
        int a[]=new int[n];
        a=s.nextIntArray(n);
        boolean t1=true;
        boolean t2=true;
        a1=a[0]-0;
        a2=n-a[0];
        for(int i=1;i<n;i++){
            if(i%2==0){
                if(t1){
                    if(a[i]-a1<0){
                        if(n-Math.abs(a[i]-a1)!=i)
                            t1=false;
                    }
                    else{
                        if(Math.abs(a[i]-a1)!=i)
                            t1=false;
                    }
                }
            }
            if(i%2!=0){
                if(t1){
                    if(Math.abs(a[i]+a1)%n!=i){
                        t1=false;
                    }
                }
            }
        }
        if(t1){
            System.out.println("YES");
            return;
        }
        for(int i=1;i<n;i++){
            if(i%2==0){
                if(t2){
                    if(Math.abs(a[i]+a2)%n!=i){
                        t2=false;
                    }
                }
            }
            if(i%2!=0){
                if(t2){
                    if(a[i]-a2<0){
                        if(n-Math.abs(a[i]-a2)!=i)
                            t2=false;
                    }
                    else{
                        if(Math.abs(a[i]-a2)!=i)
                            t2=false;
                    }
                }
            }
        }
        if(t2){
            System.out.println("YES");
            return;
        }
        System.out.println("NO");
    }





















    private static long ncr(int i, int j) {
        if(j==0){
            return 1;
        }
        int k=0;
        long ans=1;
        while(k<j){

            ans*=i-k;
            ans/=k+1;
            ans%=1000000007;
            k++;
        }
        return ans%1000000007;
    }





















    private static boolean sum(long i, int x, int y) {
        int k=0;
        while(i!=0){
            k+=i%10;
            i=i/10;
        }
        if(k<=y && k>=x)
            return true;
        else
            return false;
    }





















    private static long c(int i) {

        return 0;
    }





















    private static long gcd(long a, long b)
    {
        while (b > 0)
        {
            long temp = b;
            b = a % b; // % is remainder
            a = temp;
        }
        return a;
    }





























    public static class FasterScanner {
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;

        public int read() {
            if (numChars == -1)
                throw new InputMismatchException();
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = System.in.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }

        public String nextLine() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isEndOfLine(c));
            return res.toString();
        }

        public String nextString() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isSpaceChar(c));
            return res.toString();
        }

        public long nextLong() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            long res = 0;
            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public int nextInt() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public int[] nextIntArray(int n) {
            int[] arr = new int[n];
            for (int i = 0; i < n; i++) {
                arr[i] = nextInt();
            }
            return arr;
        }

        public long[] nextLongArray(int n) {
            long[] arr = new long[n];
            for (int i = 0; i < n; i++) {
                arr[i] = nextLong();
            }
            return arr;
        }

        private boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        private boolean isEndOfLine(int c) {
            return c == '\n' || c == '\r' || c == -1;
        }
    }
}