# Question 1:


def tempsdevol(c):
    u, n = c, 0
    while u != 1:
        if u % 2:
            u = 3*u + 1
        else:
            u = u//2
        n += 1
    return n

# Question 2


def altitude(c):
    u, umax = c, c
    while u != 1:
        if u % 2:
            u = 3*u + 1
        else:
            u = u//2
        if u > umax:
            umax = u
    return umax

# Question 3
# a)


def tempsdarret(c):
    u, n, nmax = c, 0, 0
    while u != 1:
        n += 1
        if u % 2:
            u = 3*u + 1
        else:
            u = u//2
        if u >= c:
            nmax = n
    return nmax

# b)
import time


def verification(m):# m=1000000 -> 60 sec
    start = time.time()
    for c in range(2, m+1):
        tempsdarret(c)
    return time.time() - start