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Problems

Blots on Paper

Blots on Paper

Time limit 2 seconds
Memory limit 256 MiB

Some ink was spilled on a grid paper measuring M×N cells. Each cell of the paper is now considered either pained or clean. Two painted cells belong to the same blot if there is a path from one of the cells to the other that goes through painted cells only and on each step moves from one cell to another only horizontally or vertically.

Count the number of blots and the area of the largest blot (that is, the number of cells it consists of).

Input data

The first input line contains the integers M and N (1 ≤ M, N ≤ 10^5, 1 < M·N ≤ 10^6). Each of the following M lines consists of N characters 0 or 1, where 0 denotes a clean and 1 a painted cell. There is at least one painted cell.

Output data

The only output line should contain two integers: the number of blots and the area of the largest blot.

Examples

Input example #1
6 7
1001001
1111011
1001000
1001111
0100000
0000000
Output example #1
3 13
Source NEERC Western Subregional Contest 2012