You are given an array \(A\) with \(N\) elements. You create a graph \(G\) with \(N\) vertices using \(A\) as follows:

For any pair of indices \(( i,\ j )\) where \( 1 \le i < j \le N\), if \(A[i] > A[j]\), then add an undirected edge between vertices \(i\) and \(j\).

In graph \(G\), find the maximum possible size of set \(S\) (of vertices in G) such that there exists an edge between every pair of vertices that are available in \(S\).

Input format

The first line contains an integer \(N\) denoting the number of elements in \(A\).
The second line contains \(N\) space-separated integers denoting the elements of \(A\).

Output format

Among all the vertices available in \(S\), find the maximum possible size of \(S\).

Constraints
\(1 \le N \le 10^5\)
\(1 \le A[i] \le 10^6\)