class Person:
    x = 0
    y = 0
    flu_remaining = 0
    prev_infected = False

    def __init__(self, x, y, flu_remaining=0, prev_infected=False):
        self.x = x
        self.y = y
        self.flu_remaining = flu_remaining
        self.prev_infected = prev_infected

    def distance(self, person):
        return ((self.x - person.x)**2 + (self.y - person.y)**2) ** 0.5


def flu_epidemic(mat, duration, flu_distance, flu_time, incubation_time):
    h = len(mat)
    w = len(mat[0])
    persons = []
    num_sick = 0

    for i in range(h):
        for j in range(w):
            if mat[i][j] == 'P':
                persons.append(Person(j, i))
            elif mat[i][j] == 'I':
                persons.append(Person(j, i, flu_time, True))
                num_sick += 1
    n_persons = len(persons)

    adj_mat = [[False for c in range(n_persons)]
               for r in range(n_persons)]
    for i in range(n_persons-1):
        for j in range(i+1, n_persons):
            if persons[i].distance(persons[j]) <= flu_distance:
                adj_mat[i][j] = True
                adj_mat[j][i] = True

    for t in range(0, duration+1, incubation_time):
        for i in range(n_persons):
            if persons[i].flu_remaining == 0:
                continue
            persons[i].flu_remaining -= incubation_time
            if persons[i].flu_remaining == 0:
                num_sick -= 1
                continue
            for j in range(n_persons):
                if i == j:
                    continue
                if adj_mat[i][j]:
                    if not persons[j].prev_infected:
                        persons[j].flu_remaining = flu_time
                        persons[j].prev_infected = True
                        num_sick += 1

    return num_sick