Symmetric Image Check

You are given an image of n rows and m columns. The image is represented as a matrix of pixels. Initially, every pixel is black with RGB value \((0,0,0)\).

There will be q operations. In each operation, you are allowed to change one of the three components (R, G, or B) of a single pixel. In particular, an operation is described by four values: i j c x, where i and j indicate the row and column of the pixel (1-indexed), c indicates which component to modify (1 for R, 2 for G, 3 for B), and x is the new value for that component.

After every operation, you must check whether the image is left-right symmetric. An image is left-right symmetric if for every row \(i\) and every column \(j\), the pixel at \( (i,j) \) has the same RGB value as the pixel at \( (i, m-j+1) \). In mathematical terms, for any valid \(i, j\): \[ \text{pixel}(i,j) = \text{pixel}(i, m-j+1). \]

Output Yes if the image is symmetric after an operation, or No if it is not.

inputFormat

The first line contains three integers \(n\), \(m\), and \(q\) representing the number of rows, columns, and the number of operations, respectively.

Each of the following \(q\) lines contains four values: i j c x, where \(i\) and \(j\) (1-indexed) identify a pixel, \(c\) is an integer in \(\{1,2,3\}\) representing the RGB component (1 for R, 2 for G, 3 for B), and \(x\) is the new value for that component.

outputFormat

For each operation, output a line containing either Yes if the current state of the image is left-right symmetric, or No otherwise.

sample

2 2 3
1 1 1 5
1 2 1 5
2 1 3 100

No
Yes
No