from math import sqrt, ceil, floor
from utils import parse_day

tx_min, tx_max, ty_min, ty_max = \
    map(int, parse_day(17, r'.* x=(-?\d+)..(-?\d+), y=(-?\d+)..(-?\d+)'))

vx_min = int(sqrt(tx_min * 2) - 1)
vx_max = tx_max
vy_min = ty_min
vy_max = abs(ty_min) - 1

def sum_n(n):
    return n * (n + 1) // 2

print(sum_n(vy_max))

def time_at_pos(v, d):
    """d = - (t + 1)(t - 2v) / 2 solved for t"""
    return (sqrt((2 * v + 1) ** 2 - 8 * d) + 2 * v - 1) / 2 + 1

def y_times(vy0):
    start = time_at_pos(vy0, ty_max)
    end = time_at_pos(vy0, ty_min)
    return range(ceil(start), floor(end) + 1)

def x_at(vx0, t):
    assert(t >= 0)
    return sum_n(vx0) - sum_n(max(vx0 - t, 0))

count = 0
for vy0 in range(vy_min, vy_max + 1):
    for vx0 in range(vx_min, vx_max + 1):
        for t in y_times(vy0):
            if tx_min <= x_at(vx0, t) <= tx_max:
                count += 1
                break
print(count)