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.
The first line contains integer *n* (1 ≤ *n* ≤ 1000) — the number of gears.

The second line contains *n* digits *a*<sub class="lower-index">1</sub>, *a*<sub class="lower-index">2</sub>, ..., *a*<sub class="lower-index">*n*</sub> (0 ≤ *a*<sub class="lower-index">*i*</sub> ≤ *n* - 1) — the sequence of active teeth: the active tooth of the *i*-th gear contains number *a*<sub class="lower-index">*i*</sub>.
# LUOGU_RID: 112973351
n, *a = map(int, open(0).read().split())
for i in range(n):
    a[i] = (a[i] - i) % n
for _ in range(n + 10):
    for i in range(n):
        if i % 2:
            a[i] += 1
        else:
            a[i] -= 1
        a[i] %= n
    if sum(a) == 0:
        exit(print('Yes'))
print('No')