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 Python (2.7.6) (judge verdict: Time Limit Exceeded)

from itertools import chain


N = int(raw_input())
p = map(int, raw_input().split())
# print(p)

def is_sorted(l):
    for i in xrange(0, len(l)-1):
        if l[i] != i + 1:
            return False
    return True


def is_gt(i, l):
    for e in l:
        if e > i:
            return False
    return True

def shrink(l):
    i = 1
    while i < len(l) and l[-i] == len(l)-(i-1):
        i += 1
    return l[0:-(i-1)]


j = 0
while not is_sorted(p):
    higher = [p[0]]
    lower = []
    for e in p[1:]:
        # if e >= reduce(lambda x, y: max(x, y), higher, 0):
        if is_gt(e, higher):
            higher.append(e)
        else:
            lower.append(e)
    # p = [e for e in chain(lower, higher)]
    lower.extend(higher)
    p = shrink(lower)
    # print p
    j += 1

print(j)