# USACO 2011 Nov Silver

## Problem 2. Cow Lineup

Cow Lineup
Problem 2: Cow Lineup [Brian Dean]

Farmer John has hired a professional photographer to take a picture of some of his cows. Since FJ’s cows represent a variety of different breeds, he would like the photo to contain at least one cow from each distinct breed present in his herd.

FJ’s N cows are all standing at various positions along a line, each described by an integer position (i.e., its x coordinate) as well as an integer breed ID. FJ plans to take a photograph of a contiguous range of cows along the line. The cost of this photograph is equal its size – that is, the difference between the maximum and minimum x coordinates of the cows in the range of the photograph.

Please help FJ by computing the minimum cost of a photograph in which there is at least one cow of each distinct breed appearing in FJ’s herd.

PROBLEM NAME: lineup

INPUT FORMAT:

• Line 1: The number of cows, N (1 <= N <= 50,000).

• Lines 2..1+N: Each line contains two space-separated positive integers specifying the x coordinate and breed ID of a single cow. Both numbers are at most 1 billion.

SAMPLE INPUT (file lineup.in):

6
25 7
26 1
15 1
22 3
20 1
30 1


INPUT DETAILS:

There are 6 cows, at positions 25,26,15,22,20,30, with respective breed IDs 7,1,1,3,1,1.

OUTPUT FORMAT:

• Line 1: The smallest cost of a photograph containing each distinct breed ID.

SAMPLE OUTPUT (file lineup.out):

4


OUTPUT DETAILS:

The range from x=22 up through x=26 (of total size 4) contains each of the distinct breed IDs 1, 3, and 7 represented in FJ’s herd.