1034. Forest

#include <iostream>
#include <cstring>
#include <vector>

using namespace std;

bool isForest;
bool pointTo[101];
bool visited[101];
vector<int> child[101];
int wid[101];
int n, m, maxDepth, maxWidth;

void initialize() {
	memset(pointTo, false, sizeof(pointTo));
	memset(visited, false, sizeof(visited));
	for(int i = 0; i < 101; i++) {
		child[i].clear();
	}
	isForest = true;
	maxDepth = 0;
	maxWidth = 0;
	memset(wid, 0, sizeof(wid));
}

void dfs(int father, int depth) {
	visited[father] = true;
	maxDepth = (maxDepth > depth ? maxDepth : depth);
	wid[depth]++;
	maxWidth = (maxWidth > wid[depth] ? maxWidth : wid[depth]);
	for(int i = 0; i < child[father].size(); i++) {
		dfs(child[father][i], depth + 1);
	}
}

int main() {
	while(cin >> n >> m && n != 0) {
		initialize();
		for(int i = 0; i < m; i++) {
			int tmp1, tmp2;
			cin >> tmp1 >> tmp2;
			if(pointTo[tmp2] == true || tmp1 == tmp2) {
				isForest = false;
			}
			else {
				child[tmp1].push_back(tmp2);
				pointTo[tmp2] = true;
			}
		}
		if(!isForest) {
			cout << "INVALID" << endl;
			continue;
		}
		for(int i = 1; i <= n; i++) {
			if(!pointTo[i]) {
				dfs(i, 0);
			}
		}
		for(int i = 1; i <= n; i++) {
			if(!visited[i]) {
				isForest = false;
				break;
			}
		}
		if(isForest) {
			cout << maxDepth << ' ' << maxWidth << endl;
		}
		else {
			cout << "INVALID" << endl;
		}
	}
	return 0;
}