https://www.codingame.com/ide/puzzle/horse-racing-hyperduals Casablanca’s hippodrome has grown tired of old-fashioned dual racing and has kicked it up a notch: they will now be organizing hyperduals.

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https://www.codingame.com/ide/puzzle/horse-racing-hyperduals

Casablanca’s hippodrome has grown tired of old-fashioned dual racing and has kicked it up a notch: they will now be organizing hyperduals.

During a hyperdual, only two horses will participate in the race. In order for the race to be interesting, it is necessary to try to select two horses with similar strength.

Write a program which, using a given number of strengths, identifies the two closest strengths and shows their difference with an integer.

In a hyperdual, a horse's strength is a bidimensional (Velocity,Elegance) vector. The distance between two strengths (V1,E1) and (V2,E2) is abs(V2-V1)+abs(E2-E1).

(This is a harder version of training puzzle “Horse-racing duals”. You may want to solve that problem first.)
(To date there is no specific achievement if you solve this one in pure bash. Rest assured it *is* possible nonetheless!)
Entrée
Line 1: the number N of horses
N following lines: the speed Vi and elegance Ei of each horse, space-separated
Sortie
Line 1: the distance D between the two closest strengths
Contraintes
10 ≤ N ≤ 600
0 ≤ Vi,Ei ≤ 10000000
D ≥ 0
All values are integral.
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