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 $1\leq i\leq N-1$.

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.

Constraints

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

Sample Input 1

6
3 4 1 1 2 4

Sample Output 1

3

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.

Sample Input 2

4
2 3 4 1

Sample Output 2

3

见题面 Input 部分

见题面 Output 部分