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 perform_work():
    n = int(raw_input())
    numbers = [int(x) for x in raw_input().split(" ")]

    if n == 1:
        if numbers[0] == 0:
            return True
        else:
            return False

    movements_first_to_zero = (n - numbers[0]) % n
    movements_second_to_one = round_minus(numbers[1], 1, n)
    if movements_first_to_zero != movements_second_to_one:
        return False;

    idx = 0;
    while idx < (n-2):
        dif = round_minus(numbers[idx + 2], 2, n)
        if dif != numbers[idx]:
            return False
        idx += 2

    idx = 1;
    while idx < (n-2):
        dif = round_minus(numbers[idx + 2], 2, n)
        if dif != numbers[idx]:
            return False
        idx += 2

    return True

def round_minus(first_num, second_num, base):
    if first_num > second_num:
        return first_num - second_num
    else :
        return (base - (second_num - first_num)) % base

def round_plus(first_num, second_num, base):
    if (first_num + second_num) < base:
        return first_num + second_num
    else:
        return (first_num + second_num) % base

result = perform_work()
if result:
    print "Yes"
else:
    print "No"
