Problem:
Score : 2400 points

Problem Statement

Takahashi loves sorting.

He has a permutation (p_1,p_2,...,p_N) of the integers from 1 through N. Now, he will repeat the following operation until the permutation becomes (1,2,...,N):

First, we will define high and low elements in the permutation, as follows. The i-th element in the permutation is high if the maximum element between the 1-st and i-th elements, inclusive, is the i-th element itself, and otherwise the i-th element is low.

Then, let a_1,a_2,...,a_k be the values of the high elements, and b_1,b_2,...,b_{N-k} be the values of the low elements in the current permutation, in the order they appear in it.

Lastly, rearrange the permutation into (b_1,b_2,...,b_{N-k},a_1,a_2,...,a_k).

How many operations are necessary until the permutation is sorted?

Constraints

1 ≤ N ≤ 2×10^5

(p_1,p_2,...,p_N) is a permutation of the integers from 1 through N.

Input

Input is given from Standard Input in the following format:

N
p_1 p_2 ... p_N

Output

Print the number of operations that are necessary until the permutation is sorted.

Sample Input 1

5
3 5 1 2 4

Sample Output 1

3

The initial permutation is (3,5,1,2,4), and each operation changes it as follows:

In the first operation, the 1-st and 2-nd elements are high, and the 3-rd, 4-th and 5-th are low. The permutation becomes: (1,2,4,3,5).

In the second operation, the 1-st, 2-nd, 3-rd and 5-th elements are high, and the 4-th is low. The permutation becomes: (3,1,2,4,5).

In the third operation, the 1-st, 4-th and 5-th elements are high, and the 2-nd and 3-rd and 5-th are low. The permutation becomes: (1,2,3,4,5).

Sample Input 2

5
5 4 3 2 1

Sample Output 2

4

Sample Input 3

10
2 10 5 7 3 6 4 9 8 1

Sample Output 3

6

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

/* package codechef; // don't place package name! */

import java.util.Scanner;
import java.util.ArrayList;

/* Name of the class has to be "Main" only if the class is public. */
public class Main
{
	public static void main (String[] args) throws java.lang.Exception
	{
		// your code goes here
		Scanner sn = new Scanner(System.in);
		ArrayList<Integer> list = new ArrayList<Integer>();
		
		String str = sn.nextLine();
		String[] s = sn.nextLine().split(" ");
		int[] nums = new int[s.length];
		int[] nextArray;
		int count = 0;
		for(int i = 0;i<nums.length;i++){
		    nums[i] = Integer.parseInt(s[i]);
		}
		
		boolean flag = true;
		while(flag){
		    count++;
		    
		    int max = 0;
		    int frontcount = 0;
		    nextArray = new int[nums.length];
		    list = new ArrayList<Integer>();
		    
		    for(int i = 0;i<nums.length;i++){
		        max = Math.max(max, nums[i]);
		        if(max != nums[i]){         //nums[i]が高い項のとき
		            nextArray[frontcount++] = nums[i]; 
		        }else{                      //低いとき
		            list.add(new Integer(i));
		        }
		    }
		    int size = list.size();
		    for(int i = 0;i<size;i++){
		        nextArray[frontcount++] = nums[list.get(i)];
		    }
		    
		    //nextArrayは昇順か
		    boolean isAscending = true;
		    for(int i = 0;i<nextArray.length-1;i++){
		        if(nextArray[i] > nextArray[i+1]){
		            isAscending = false;
		            break;
		        }
		    }
		    if(isAscending){
		        flag = false;
		    }
		    nums = nextArray;
		}
		System.out.println(count);
	}
}