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B. Flag of Berland
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

The flag of Berland is such rectangular field n × m that satisfies following conditions:

• Flag consists of three colors which correspond to letters 'R', 'G' and 'B'.
• Flag consists of three equal in width and height stripes, parralel to each other and to sides of the flag. Each stripe has exactly one color.
• Each color should be used in exactly one stripe.

You are given a field n × m, consisting of characters 'R', 'G' and 'B'. Output "YES" (without quotes) if this field corresponds to correct flag of Berland. Otherwise, print "NO" (without quotes).

Input

The first line contains two integer numbers n and m (1 ≤ n, m ≤ 100) — the sizes of the field.

Each of the following n lines consisting of m characters 'R', 'G' and 'B' — the description of the field.

Output

Print "YES" (without quotes) if the given field corresponds to correct flag of Berland . Otherwise, print "NO" (without quotes).

Examples
Input
6 5RRRRRRRRRRBBBBBBBBBBGGGGGGGGGG
Output
YES
Input
4 3BRGBRGBRGBRG
Output
YES
Input
6 7RRRGGGGRRRGGGGRRRGGGGRRRBBBBRRRBBBBRRRBBBB
Output
NO
Input
4 4RRRRRRRRBBBBGGGG
Output
NO
Note

The field in the third example doesn't have three parralel stripes.

Rows of the field in the fourth example are parralel to each other and to borders. But they have different heights — 2, 1 and 1.