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.
import java.io.*;
import java.util.*;
import java.math.*;
public class code310_2B
{
    public static void main(String args[])
    {
        InputReader in=new InputReader(System.in);
        PrintWriter out=new PrintWriter(System.out);
        int n=in.readInt();
        int[] a=new int[n];
        int[] b=new int[n];
        for(int i=0;i<n;i++)
            a[i]=in.readInt();
        int min=Integer.MAX_VALUE;
        for(int i=0;i<n;i++){
            if(i%2==0){
                if(a[i]>i)
                    b[i]=n-a[i]+i;
                else if(a[i]<i)
                    b[i]=i-a[i];
                else if(a[i]==i)
                    b[i]=0;
                if(b[i]<min)
                    min=b[i];
            }else{
                if(a[i]>i)
                    b[i]=a[i]-i;
                else if(a[i]<i)
                    b[i]=a[i]+n-i;
                else if(a[i]==i)
                    b[i]=0;
                if(b[i]<min)
                    min=b[i];                
            }
            //out.println(b[i]);
        }
        int gcd=b[0];
        for(int i=1;i<n;i++)
            gcd=gcd(gcd,b[i]);
        if(gcd==min)
            out.println("Yes");
        else out.println("No");
        out.flush();
    }
    public static int gcd(int a, int b)
    {
        while(b>0)
        {
            int t=b;
            b=a%b;
            a=t;
        }
        return a;
    }
}
class InputReader
{
    private InputStream stream;
    private byte[] buf=new byte[1024];
    private int curChar;
    private int numChars;
    private SpaceCharFilter filter;
    public InputReader(InputStream stream)
    {this.stream=stream;}
    public int read()
    {
        if(numChars==-1)
        throw new InputMismatchException();
        if(curChar>=numChars)
        {
            curChar=0;
            try{
                numChars=stream.read(buf);
            }catch(IOException e){
                throw new InputMismatchException();
            }
            if(numChars<=0)
            return -1;
        }
        return buf[curChar++];
    }
    public int readInt()
    {
        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 long readLong()
    {
        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[] readArray(int len)
    {
        int c=read();
        while(isSpaceChar(c))
            c=read();
        int sgn=1;
        if(c=='-')
        {
            sgn=-1;
            c=read();
        }
        int[] res=new int[len];int j=0;
        do{
            if(c<'0'||c>'9')
            throw new InputMismatchException();
            //res*=10;
            res[j++]=c-'0';
            c=read();
        }while(!isSpaceChar(c));
        return res;
    }
    public String readString()
    {
        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 boolean isSpaceChar(int c)
    {
        if(filter!=null)
            return filter.isSpaceChar(c);
        return c==' '||c=='\n'||c=='\r'||c=='\t'||c==-1;
    }
    public String next()
    {
        return readString();
    }
    public interface SpaceCharFilter
    {
        public boolean isSpaceChar(int ch);
    }
}