Band **K** consists of ~4~ members:
**HG**,
**NI**,
**RY**, and
**IK**. Apart from
practicing and making music, the band occasionally organizes some
recreational activities to bring the members closer together and
increase the band's solidarity.

Today, they decided to play hide and seek, and this time they will play on the schoolyard. The schoolyard can be considered as a grid with size ~n \times m~, with rows numbered from ~1~ to ~n~, and columns numbered from ~1~ to ~m~. When viewed from above, the cell at row ~i~ and column ~j~ has color ~c_{i,j}~.

Due to her shy and timid personality, **HG**
is chosen to be the one who hides. Understanding **HG**'s personality,
the other three members **NI**,
**RY**, and
**IK** guess that
**HG** will curl up into a *stone*.
This *stone* will have the shape of a ~2 \times 2~ square and will
occupy ~4~ cells on the schoolyard.

Furthermore, this *stone* will have a very distinctive color. The
*stone* will have ~3~ distinct colors, such that the color of ~2~ cells
in the second column are the same. Specifically, if the stone occupies
~4~ cells ~(i, j)~, ~(i + 1, j)~, ~(i, j + 1)~, and ~(i + 1, j + 1)~,
then:

~c_{i, j} \ne c_{i + 1, j}~,

~c_{i, j} \ne c_{i, j + 1}~,

~c_{i + 1, j} \ne c_{i + 1, j + 1}~,

~c_{i, j + 1} = c_{i + 1, j + 1}~.

Illustration for the fourth example. The highlighted square in the
figure represents a valid *stone* of **HG**.

You are given the colors of the cells on the schoolyard. Determine
whether **HG** is hiding on the schoolyard or not.

#### Input

The first line contains two integers ~n~ and ~m~ (~2 \le n, m \le 500~) – the size of the schoolyard.

The ~i~-th line of the next ~n~ lines contains a string of length ~m~ consisting of uppercase English letters. The ~j~-th character represents the color ~c_{i, j}~.

#### Output

Print "YES" if
there exists a ~2 \times 2~ square on the schoolyard that matches the
description of **HG**'s *stone*. Otherwise, print
"NO".

#### Scoring

The score for this problem is ~500~ points.

#### Sample Input 1

```
2 2
BP
YP
```

#### Sample Output 1

```
YES
```

#### Sample Input 2

```
3 3
VOI
IOI
TST
```

#### Sample Output 2

```
YES
```

#### Sample Input 3

```
5 5
QWERT
YUIOP
ASDFG
HJKLZ
XCVBN
```

#### Sample Output 3

```
NO
```

#### Sample Input 4

```
16 16
WWWWWWWWWWWWWWWW
WPPWWWWWWWWWWWWW
PWWPWWWPPWWWWWWW
WWWWBPPPPPPWWWWW
WWWWYPPPPPPPWWWW
WWWPPPPPPPPPPWWW
WWWPGGGPPGGGPWWW
WWWPPPGPPGPPPWWW
WWWPPGPPPPGPPWWW
WWWPGPPPPPPGPWWW
WWWPBPPPPPPBPWWW
WWPPPPPPPPPPPPWW
WWPPPPPPPPPPPPWW
WPPPPWPPPPWPPPPW
WPPPWWWPPWWWPPPW
WWWWWWWWWWWWWWWW
```

#### Sample Output 4

```
YES
```

#### Notes

In the first example, the schoolyard has size ~2 \times 2~. There is
only one ~2 \times 2~ square on the schoolyard that matches the
description of **HG**'s *stone*.

The fourth example has an illustration in the problem statement.

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