Problem Description
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).
Input
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.
[Technical Specification]
1≤n≤100000
0≤ai≤1000000000
Output
For each case，.output the answer in a single line.
Sample Input
3
1 2 3
2
2 1
Sample Output
1
3
