module Program

open System

let solve a =
    let len = a |> Array.length
    let a' =
        let comp =
            a
            |> Array.sort
            |> Array.indexed 
            |> Array.map (fun (idx, x) -> (x, idx))
            |> Map.ofArray
        a 
        |> Array.map (fun x -> comp.[x] + 1)
    
    let dp = Array.zeroCreate (len + 1)
    a' |> Array.iter (fun a -> dp.[a] <- dp.[a-1] + 1)
    len - (dp |> Array.max)

let N = Console.ReadLine() |> ignore
let a = 
    Console.ReadLine().Split()
    |> Array.map int

solve a
|> Console.WriteLine