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USACO $2023$ December Contest, Silver

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Problem $1.$ Bovine ACrobatics

Time Remaining: $3hrs,59$min,$46sec$

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English $($en$)vv$

Farmer John has decided to make his cows do some acrobatics! First, FJ weighs his cows and finds that they have $N(1N2*{10}^5)$ distinct weights. In particular, for each iin$[1,N],a_i$ of his cows have a weight of