Background

Given two integers $n$ and $m$, you need to construct a matrix $M$ satisfying the following constraints:

  • The number of rows and columns of $M$ are $n$ and $m$ respectively.

  • The matrix contains only 0s and 1s, namely, $M_{i,j} ∈ 0, 1 for all 1 ≤ i ≤ n and 1 ≤ j ≤ m.$

  • The number of mixed subrectangles equal to the number of pure subrectangles. The subrectangles containing   both $0$s and $1$s are considered mixed subrectangles, otherwise pristine subrectangles. Note that a subrectangle   intersects some consecutive rows and some consecutive columns.

Now contestants have submitted many matrices, you need to check if they are right or not.

Input

The first line contains two integers $n$ and $m (1 ≤ n, m ≤ 10^6, 1 ≤ n × m ≤ 10^6)$, denoting the number of rows and columns respectively.

Then next n lines, each line has m digits denoting the matrix. .

Output

Print $3$ integers in one line, denoting the number of mixed subrectangles, pure $0$s subrectangles, pure $1$s subrectangles.

Samples

2 3
0 1 1
1 1 0

9 2 7