22180_Fores

In the field of computer science, forest is important and deeply researched, it is a model for many data structures. Now it's your job here to calculate the depth and width of given forests.

Precisely, a forest here is a directed graph with neither loop nor two edges pointing to the same node. Nodes with no edge pointing to are roots, we define that roots are at level 0. If there's an edge points from node A to node B, then node B is called a child of node A, and we define that B is at level (k+1) if and only if A is at level k.

We define the depth of a forest is the maximum level number of all the nodes, the width of a forest is the maximum number of nodes at the same level.

There're several test cases. For each case, in the first line there are two integer numbers n and m ( 1 ≤ n ≤ 100,  0 ≤ m ≤ 100,  m ≤ n*n ) indicating the number of nodes and edges respectively, then m lines followed, for each line of these m lines there are two integer numbers a and b ( 1 ≤ a, b ≤ n ) indicating there's an edge pointing from a to b. Nodes are represented by numbers between 1and n.

n=0 indicates end of input.

For each case output one line of answer, if it's not a forest, i.e. there’s at least one loop or two edges pointing to the same node, output "INVALID" (without quotation mark), otherwise output the depth and width of the forest, separated by a white space.

1 0
1 1
1 1
3 1
1 3
2 2
1 2
2 1
0 88

0 1
INVALID
1 2
INVALID