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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.
20 4 1 10 7 5 19 7 3 12 8 11 15 12
Query 3 ("3 12 8") is the first that is inconsistent with those before it. From queries 1 and 2 and the fact that all hay stacks have a distinct number of bales, we deduce that one of stacks 5..10 must contain exactly 7 bales. However, this stack contradicts the answer to query 3.