from math import log, exp

T = 100
N = 100


def kernel(t, mu):
    return mu * exp(-mu * t)


def base_rate(t, lamb):
    return lamb


def ll(crimes, weights, mu, lamb):
    r = 0
    for i, crime in enumerate(crimes):
        t, v = crime
        a = sum(weights[(u, v)] * kernel(t - s, mu) for s, u in crimes[:t])
        r += log(base_rate(t, lamb) + a)
    for j in range(N):
        a = sum(weights[(u, v)] * kernel(T - s, mu) for s, u in crimes)
        r -= log(a)