Problem Statement

You are given a sequence $A=(A_1,A_2,\ldots,A_N)$ of length $N$, consisting of integers between $1$ and $4$.

Takahashi may perform the following operation any number of times (possibly zero):

• choose a pair of integer $(i,j)$ such that $1\leq i<j\leq N$, and swap $A_i$ and $A_j$.

Find the minimum number of operations required to make $A$ non-decreasing. A sequence is said to be non-decreasing if and only if $A_i\leq A_{i+1}$ for all $1\leq i\leq N-1$.

Constraints

• $2 \leq N \leq 2\times 10^5$
• $1\leq A_i \leq 4$
• All values in the input are integers.

Input

The input is given from Standard Input in the following format:

N
A_1 A_2 \ldots A_N

Output

Print the minimum number of operations required to make $A$ non-decreasing in a single line.