AtCoder Grand Contest 014 - Strange Sorting

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.

Examples

Input

5
3 5 1 2 4


Output

3


Input

5
5 4 3 2 1


Output

4


Input

10
2 10 5 7 3 6 4 9 8 1


Output

6

Source: atcoder | Difficulty: UNKNOWN_DIFFICULTY


Solutions:
N = int(input())
P = list(map(int, input().split()))
if N == 1:
	print(0)
	exit()
Pi = [0] * (N + 1)
for (i, n) in enumerate(P, 1):
	Pi[n] = i
T = [0] * N
f = [0] * N
if Pi[N] > Pi[N - 1]:
	T[N - 1] = 0
	f[N - 1] = N - 1
else:
	T[N - 1] = 1
	f[N - 1] = N
for i in range(N - 2, 0, -1):
	if T[i + 1] == 0:
		i_i = Pi[i]
		i_ii = Pi[i + 1]
		if i_ii > i_i:
			T[i] = T[i + 1]
			f[i] = f[i + 1]
		else:
			T[i] = T[i + 1] + 1
			f[i] = i + 1
	else:
		i_f = Pi[f[i + 1]]
		i_i = Pi[i]
		i_ii = Pi[i + 1]
		if i_f < i_i < i_ii or i_ii < i_f < i_i or i_i < i_ii < i_f:
			T[i] = T[i + 1]
			f[i] = f[i + 1]
		else:
			T[i] = T[i + 1] + 1
			f[i] = i + 1
print(T[1])


N = int(input())
P = list(map(int, input().split()))
P2 = [0] * (N + 1)
i = N - 1
T = 0
for j in range(N):
	P2[P[j]] = j + 1
while i >= 0:
	if P2[i] > P2[i + 1]:
		T = 1
		f = i + 1
		i = i - 1
		break
	i = i - 1
while i > 0:
	if (P2[i + 1] - P2[i]) * (P2[i] - P2[f]) * (P2[f] - P2[i + 1]) > 0:
		T = T + 1
		f = i + 1
	i = i - 1
print(T)


(N, *P) = map(int, open(0).read().split())
I = {P[i]: i + 1 for i in range(N)}
I[0] = T = f = 0
while N > 1:
	x = I[f]
	y = I[N - 1]
	z = I[N]
	if (z > y) ^ (y > x) ^ (x > z):
		T += 1
		f = N
	N -= 1
print(T)


N = int(input())
P = list(map(int, input().split()))
Pi = [0] * (N + 1)
for (i, n) in enumerate(P, 1):
	Pi[n] = i
i = N - 1
T = 0
f = 0
while i:
	i_f = Pi[f]
	i_i = Pi[i]
	i_ii = Pi[i + 1]
	if i_f < i_ii < i_i or i_i < i_f < i_ii or i_ii < i_i < i_f:
		T += 1
		f = i + 1
	i -= 1
print(T)