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 (Python):
N,*P=map(int,open(0).read().split());I={P[i]:i+1for 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)

Solution (Python):
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)

Solution (Python):
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])

Solution (Python):

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)