Problem:
Score : 500 points

Problem Statement

You are given a sequence (P_1,P_2,...,P_N) which is a permutation of the integers from 1 through N.
You would like to sort this sequence in ascending order by repeating the following operation:

Choose an element in the sequence and move it to the beginning or the end of the sequence.

Find the minimum number of operations required.
It can be proved that it is actually possible to sort the sequence using this operation.

Constraints

1 \leq N \leq 2\times 10^5

(P_1,P_2,...,P_N) is a permutation of (1,2,...,N).

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
P_1
:
P_N

Output

Print the minimum number of operations required.

Sample Input 1

4
1
3
2
4

Sample Output 1

2

For example, the sequence can be sorted in ascending order as follows:

Move 2 to the beginning. The sequence is now (2,1,3,4).

Move 1 to the beginning. The sequence is now (1,2,3,4).

Sample Input 2

6
3
2
5
1
4
6

Sample Output 2

4

Sample Input 3

8
6
3
1
2
7
4
8
5

Sample Output 3

5

Solution in Rust (1.15.1) (judge verdict: Accepted)

fn lower_bound<T: std::cmp::Ord>(arr: &Vec<T>, b: T) -> usize {
    let (mut lt, mut ge) = (0, arr.len());
    // lt=-1にすると型強制しなきゃなのでここで確かめる
    if arr[lt] >= b {
        return 0;
    }
    while lt + 1 < ge {
        let m = (lt + ge) / 2;
        if arr[m] < b {
            lt = m;
        } else if arr[m] > b {
            ge = m;
        } else {
            return m;
        }
    }
    ge
}

fn main() {
    let n = read();
    let mut p: Vec<usize> = vec![];
    for _ in 0..n {
        p.push(read());
    }
    let mut q = vec![0; n];
    for i in 0..n {
        q[p[i] - 1] = i;
    }
    let mut prev = std::usize::MAX;
    let mut cont = 1;
    let mut anss = 0;
    for i in 0..n {
        if prev < q[i] {
            cont += 1;
        } else {
            cont = 1;
        }
        prev = q[i];
        anss = max(anss, cont);
    }
    println!("{}", n - anss);

    // let mut dp = vec![std::usize::MAX; n];
    // let mut ans = 0;
    // for i in 0..n {
    //     let b = lower_bound(&dp, v[i]);
    //     dp[b] = v[i];
    //     ans = max(ans, b + 1);
    // }
    // println!("{}", n - ans);
}

// =========
#[allow(unused_imports)]
use std::cmp::{max, min};
#[allow(unused_imports)]
use std::collections::{HashMap, HashSet};
#[allow(unused_imports)]
use std::process::exit;

#[allow(dead_code)]
const MOD: usize = 1000000007;

fn read<T: std::str::FromStr>() -> T {
    use std::io::Read;
    let stdin = std::io::stdin();
    let stdin = stdin.lock();
    let token: String = stdin
        .bytes()
        .map(|c| c.expect("failed to read char") as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().expect("failed to parse token")
}

// =========