A numeric sequence of ai is ordered if a1<a2<…<aN. Let the subsequence of the given numeric sequence (a1,a2,…,aN) be any sequence (ai1,ai2,…,aiK), where 1≤i1<i2<…<iK≤N. For example, sequence (1, 7, 3, 5, 9, 4, 8) has ordered subsequences, eg. (1, 7), (3, 4, 8) and many others.
S[ i , j ] indicates ( ai,ai+1,ai+2,…,aj) .
Your program, when given the numeric sequence (a1,a2,…,aN), must find the number of pair ( i, j) which makes the length of the longest ordered subsequence of S[ i , j ] equals to the length of the longest ordered subsequence of (a1,a2,…,aN).
Multi test cases (about 100), every case occupies two lines, the first line contain n, then second line contain n numbers a1,a2,…,aN separated by exact one space.
Process to the end of file.
For each case，.output the answer in a single line.
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