## USACO 2013 US Open, Gold

## Problem 1. Photo

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Problem 1: Photo [Brian Dean, 2013]
Farmer John has decided to assemble a panoramic photo of a lineup of his N
cows (1 <= N <= 200,000), which, as always, are conveniently numbered
from 1..N. Accordingly, he snapped M (1 <= M <= 100,000) photos, each
covering a contiguous range of cows: photo i contains cows a_i through b_i
inclusive. The photos collectively may not necessarily cover every single cow.
After taking his photos, FJ notices a very interesting phenomenon: each
photo he took contains exactly one cow with spots! FJ was aware that he
had some number of spotted cows in his herd, but he had never actually
counted them. Based on his photos, please determine the maximum possible
number of spotted cows that could exist in his herd. Output -1 if there
is no possible assignment of spots to cows consistent with FJ's
photographic results.
PROBLEM NAME: photo
INPUT FORMAT:
* Line 1: Two integers N and M.
* Lines 2..M+1: Line i+1 contains a_i and b_i.
SAMPLE INPUT (file photo.in):
5 3
1 4
2 5
3 4
INPUT DETAILS:
There are 5 cows and 3 photos. The first photo contains cows 1 through 4, etc.
OUTPUT FORMAT:
* Line 1: The maximum possible number of spotted cows on FJ's farm, or
-1 if there is no possible solution.
SAMPLE OUTPUT (file photo.out):
1
OUTPUT DETAILS:
From the last photo, we know that either cow 3 or cow 4 must be spotted.
By choosing either of these, we satisfy the first two photos as well.

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