1034 - Haybale Guessing

Time Limit: 2s Memory Limit: 128MB

Submissions: 11 Solved: 4
Description
The cows, who always have an inferiority complex about their intelligence, have a new guessing game to sharpen their brains. A designated 'Hay Cow' hides behind the barn and creates N (1 <= N <= 1,000,000) uniquely-sized stacks (conveniently numbered 1..N)of hay bales, each with 1..1,000,000,000 bales of hay. The other cows then ask the Hay Cow a series of Q (1 <= Q <= 25,000)questions about the the stacks, all having the same form: What is the smallest number of bales of any stack in the range of stack numbers Ql..Qh (1 <= Ql <= N; Ql <= Qh <= N)? The Hay Cow answers each of these queries with a single integer A whose truthfulness is not guaranteed. Help the other cows determine if the answers given by the Hay Cow are self-consistent or if certain answers contradict others.
Input
* Line 1: Two space-separated integers: N and Q * Lines 2..Q+1: Each line contains three space-separated integers that represent a single query and its reply: Ql, Qh, and A
Output
* Line 1: Print the single integer 0 if there are no inconsistencies among the replies (i.e., if there exists a valid realization of the hay stacks that agrees with all Q queries). Otherwise,print the index from 1..Q of the earliest query whose answer is inconsistent with the answers to the queries before it.
Sample Input
20 4
1 10 7
5 19 7
3 12 8
11 15 12
Sample Output
3
Hint
Source
USACO JAN08