6003번 - Claustrophobic Cows 다국어

문제

Farmer John has acquired a set of N (2 <= N <= 2,000) touchy cows who are conveniently numbered 1..N. They really hate being too close to other cows. A lot.

FJ has recorded the integer X_i,Y_i coordinates of every cow i (1 <= X_i <= 100,000; 1 <= Y_i <= 100,000).

Among all those cows, exactly two of them are closest together. FJ would like to spread them out a bit. Determine which two are closest together and print their cow id numbers (i) in numerical order.

By way of example, consider this field of cows (presented on a typewriter grid that has slightly different proportions than you might expect):

 10 | . . . . . . . 3 . . . . .
 9 | . 1 . . 2 . . . . . . . .
 8 | . . . . . . . . . . . . .
 7 | . . . . . . . . . . 4 . .
 6 | . . . . . . 9 . . . . . .
 5 | . 8 . . . . . . . . . . .
 4 | . . . . . 7 . . . . . . .
 3 | . . . . . . . . . 5 . . .
 2 | . . . . . . . . . . . . .
 1 | . . . . 6 . . . . . . . .
 0 ---------------------------
 1 1 1 1
 0 1 2 3 4 5 6 7 8 9 0 1 2 3

Quick visual inspection shows that cows 7 and 9 are closest together (the distance separating them is sqrt(1*1+2*2) = sqrt(5), so the output would be '7 9' on a single line (without quotes, of course).

입력

• Line 1: A single integer: N
• Lines 2..N+1: Line i contains the coordinates of cow i expressed as two space-separated integers: X_i and Y_i

출력

• Line 1: The two numerical IDs of the closest pair of cows (sorted)

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