Consider an $N \times N$ matrix. Let us denote by a_{i, j} the entry in the i-th row and j-th column. For a_{i, j} where i=1 or j=1 holds, its value is one of 0, 1 and 2 and given in the input. The remaining entries are defined as follows:
- $a_{i,j} = \mathrm{mex}(a_{i-1,j}, a_{i,j-1}) (2 \leq i, j \leq N)$ where $\mathrm{mex}(x, y)$ is defined by the following table:$\mathrm{mex}(x, y)y=0y=1y=2x=0121x=1200x=2100$
How many entries of the matrix are 0, 1, and 2, respectively?

-----Constraints-----
- $1 \leq N \leq 500{,}000$
- a_{i,j}'s given in input are one of 0, 1 and 2.

-----Input-----
Input is given from Standard Input in the following format:
N
a_{1, 1} a_{1, 1} ... a_{1, N}
a_{2, 1}
:
a_{N, 1}

-----Output-----
Print the number of 0's, 1's, and 2's separated by whitespaces.

-----Sample Input-----
4
1 2 0 2
0
0
0

-----Sample Output-----
7 4 5

The matrix is as follows:
1 2 0 2
0 1 2 0
0 2 0 1
0 1 2 0

见题面

见题面