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 $1\leq i \lt j\leq N$, 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 $1\leq i\leq N-1$.

The input is given from Standard Input in the following format: >$N$\ >$A_1$ $A_2$ $\ldots$ $A_N$ #### Constraints - $2 \leq N \leq 2\times 10^5$ - $1\leq A_i \leq 4$ - All values in the input are integers.

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

***For Sample #1:*** One can make $A$ non-decreasing with the following three operations: - Choose $(i,j)=(2,3)$ to swap $A_2$ and $A_3$, making $A=(3,1,4,1,2,4)$. - Choose $(i,j)=(1,4)$ to swap $A_1$ and $A_4$, making $A=(1,1,4,3,2,4)$. - Choose $(i,j)=(3,5)$ to swap $A_3$ and $A_5$, making $A=(1,1,2,3,4,4)$. This is the minimum number of operations because it is impossible to make $A$ non-decreasing with two or fewer operations. Thus, $3$ should be printed.

AtCoder [ABC302G]