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.util.*;
import java.io.*;

/**
 * @author Deepit-PC
 *
 */
public class CaseOfFakeNumbers {
    public static InputReader in;
    public static PrintWriter out;

    public static final int MOD = (int) (1e9 + 7);

    public static void main(String[] args) {
	in = new InputReader(System.in);
	out = new PrintWriter(System.out);
	
	int n = in.nextInt();
	String result = "No";
	int[] a = in.nextIntArray(n);
	for (int steps = 0; steps <= n; steps++) {
	    for (int i = 0; i < n; i++) {
		if((i&1) == 0) {
		    a[i]++;
		    if(a[i] == n) {
			a[i] = 0;
		    }
		} else {
		    a[i]--;
		    if(a[i] == -1) {
			a[i] = n - 1;
		    }
		}
	    }
	    boolean found = true;
	    for (int i = 0; i < n; i++) {
		found &= (a[i] == i);
	    }
	    if(found) {
		result = "Yes";
		break;
	    }
	}
	out.println(result);
	
	out.close();
    }

    static class Node implements Comparable<Node> {
	int next;
	int dist;

	public Node(int u, int v) {
	    this.next = u;
	    this.dist = v;
	}

	public void print() {
	    out.println(next + " " + dist + " ");
	}

	public int compareTo(Node that) {
	    return Integer.compare(this.next, that.next);
	}
    }

    static class InputReader {

	private InputStream stream;
	private byte[] buf = new byte[8192];
	private int curChar, snumChars;
	private SpaceCharFilter filter;

	public InputReader(InputStream stream) {
	    this.stream = stream;
	}

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

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

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

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

	public String readString() {
	    int c = snext();
	    while (isSpaceChar(c))
		c = snext();
	    StringBuilder res = new StringBuilder();
	    do {
		res.appendCodePoint(c);
		c = snext();
	    } 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 interface SpaceCharFilter {
	    public boolean isSpaceChar(int ch);
	}
    }
}
