human
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.
#!/us
assistant
#Here is Python program to print "Yes" (without the quotes), if the given Stolp's gears puzzle is real, and "No" (without the quotes) otherwise.
r/bin/env python
# 556B_fake.py - Codeforces.com 556B Fake quiz
#
# Copyright (C) 2015 Sergey
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#       http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.

"""
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
"""

# Standard libraries
import unittest
import sys
import re

# Additional libraries

###############################################################################
# Fake Class
###############################################################################

class Fake:
    """ Fake representation """

    def __init__(self, args):
        """ Default constructor """

        self.list = args
        self.n = len(self.list)

    def rotate(self):
        for i in range(self.n):
            if not i % 2:
                self.list[i] += 1
            else:
                self.list[i] -= 1
            self.list[i] %= self.n

    def calculate(self):
        """ Main calcualtion function of the class """
        result = 0
        for i in range(self.n):
            prev = -1
            match = 1
            for n in self.list:
                if n == prev + 1:
                    pass
                else:
                    match = 0
                prev = n
            if match:
                result = 1
       ...