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.
#!/usr/bin/env python
# -*- coding: utf-8 -*-

import sys


def read_in():
    lines = list()
    for line in sys.stdin:
        line = line.replace('\n', '')
        lines.append(line)
    # print lines
    return lines


def toy_cars(lines):
    lines = lines[1:]
    # print lines
    good_set = set()
    bad_set = set()
    for i in range(len(lines)):
        cul_list = lines[i].split(' ')
        for j in range(len(cul_list)):
            if cul_list[j] == '-1':
                if len(lines) == 1 and len(cul_list) == 1:
                    good_set.add(i+1)
                pass
            elif cul_list[j] == '0':
                good_set.add(i+1)
                good_set.add(j+1)
            elif cul_list[j] == '1':
                good_set.add(j+1)
                bad_set.add(i+1)
                pass
            elif cul_list[j] == '2':
                good_set.add(i+1)
                bad_set.add(j+1)
                pass
            elif cul_list[j] == '3':
                bad_set.add(i+1)
                bad_set.add(j+1)
                pass
            else:
                raise Exception
    result = good_set - bad_set
    sorted_result = sorted(result)
    # print result
    print len(sorted_result)
    for x in sorted_result:
        print x,


def ZerosAndOnes():
    n = int(raw_input())
    a = raw_input()
    print abs(a.count('1')-a.count('0'))


def FakeNumbers():
    n = int(raw_input())
    a = raw_input()
    check = list()
    for i in range(n):
        check.append(str(i))
    # print check
    a = a.split(' ')
    v = 'No'
    for j in range(n):
        if check == a:
            v = 'Yes'
        for i in range(n):
            if a[i] == ' ':
                continue
            if i % 2 == 0:
                a[i] = str(int(a[i]) + 1)
            else:
                a[i] = str(int(a[i]) - 1)
            if int(a[i]) < 0:
                a[i] = str(n - 1)
            if not int(a[i]) < n:
                a[i] = '0'
        # print a
    print v


def main():
    # lines = read_in()
    # print lines
    # toy_cars(lines)
    # ZerosAndOnes()
    FakeNumbers()


if __name__ == '__main__':
    main()
