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.
##def _equi(_s1:list, _s2:list) -> bool:
##    _s1.sort()
##    _s2.sort()
##    if _s1 == _s2:
##        return True
##    return False
##
##s1, s2 = input(), input()
##
##if s1 == s2:
##    print('YES')
##else:
##    if (_equi(list(s1[:len(s1)//2]), list(s2[:len(s2)//2]))\
##        and _equi(list(s1[len(s1)//2:]), list(s2[len(s2)//2:])))\
##        or (_equi(list(s1[:len(s1)//2]), list(s2[len(s2)//2:]))\
##        and _equi(list(s1[len(s1)//2:]), list(s2[:len(s2)//2]))):
##        print('YES')
##    else:
##      print('NO')

def check_order(_list:list) -> bool:
    for i in range(len(_list)):
        if _list[i] != i:
            return False
    return True

def check_repe(current_list:list, lib_list:[list]) -> bool:
    if current_list in lib_list:
        return True
    return False

def _up_push(x:int, maxi:int) -> int:
    if x+1 == maxi:
        return 0
    return x+1

def _down_push(x:int, maxi:int) -> int:
    if x == 0:
        return maxi-1
    return x-1

def move(_list:list) -> list:
    temp_list = []
    for i in range(len(_list)):
        if i%2 == 0:
           temp_list.append(_up_push(_list[i], len(_list)))
        else:
            temp_list.append(_down_push(_list[i], len(_list)))
    return temp_list


number = int(input())
gear_list = list(map(int, input().split()))

lib = []
lib.append(gear_list)

if gear_list == [0] or check_order(gear_list):
    print('Yes')
else:
    while 1:
        gear_list = move(gear_list)
        if check_repe(gear_list, lib):
            status = 'repetition'
            break
        lib.append(gear_list)
        if check_order(gear_list):
            print('Yes')
            break

try:
    if status == 'repetition':
        print('No')
except NameError:
    pass
