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 sys
n = int(input())
a = list(map(int, input().split()))
even = a[::2]
odd = a[1::2]
ans = 0
if n == 2 and len(set(a)) == 1:ans = 1
if (len(even) != len(set(even))) or  (len(odd) != len(set(odd))):
    ans = 1
if n < 7:
    kl = [i for i in range(n)]
    for i in range(6*120):
        
        if kl == a:
            print("Yes")
            sys.exit(0)
        else:
            for j in range(n):
                if j%2 == 0:
                    a[j] += 1
                    a[j] %= n
                else:
                    a[j] -= 1
                    a[j] %= n

    print("No")
    sys.exit(0)
de = 0
def rotdiff(x, y):
    if (x + 2)%n == y:
        return True
    return False
def nordiff(x, y):
    if (x - 2)%n == y:
        return True
    return False
if ans != 1:
    for i in range(len(even) - 1):
        if de == 0:
            if nordiff(even[i], even[i+1]):
                de = 1
            elif rotdiff(even[i], even[i+1]):
                de = -1
            else:
                ans = 1
                break
        else:
            if de == 1:
                if not nordiff(even[i], even[i+1]):
                    ans = 1
            else:
                if not rotdiff(even[i], even[i+1]):
                    ans = 1
    de = 0
    for i in range(len(odd) - 1):
        if de == 0:
            if nordiff(odd[i], odd[i+1]):
                de = 1
            elif rotdiff(odd[i], odd[i+1]):
                de = -1
            else:
                ans = 1
                break
        else:
            if de == 1:
                if not nordiff(odd[i], odd[i+1]):
                    ans = 1
            else:
                if not rotdiff(odd[i], odd[i+1]):
                    ans = 1
print('No' if ans else 'Yes')
