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
$1 \le N \le 10^5$ 
$1 \le A[i] \le 10^6$