You are given an array of nn integers a1,a2,...,ana1,a2,...,an. We define that a sequence p1,p2,...,pk(k∈[1,n])p1,p2,...,pk(k∈[1,n]) is beautiful if and only if these conditions are met:
∙∙ 1≤p1<p2<⋯<pk≤n.1≤p1<p2<⋯<pk≤n.
∙∙ There exists t(t∈[1,k])t(t∈[1,k]) satisfying ap1<ap2<⋯<aptap1<ap2<⋯<apt and apt>apt+1>⋯>apkapt>apt+1>⋯>apk.
You need to find all the longest beautiful sequences, and output the lexicographically smallest one and the lexicographically largest one in them.
Check the examples below for better understanding.