726 B | 726 chars
import sys
from math import sqrt, pi, sin, factorial, ceil, floor
from datetime import datetime, timedelta
BLANK = " "
# inp = input
inp = lambda : sys.stdin.readline()[:-1].strip()
mii = lambda x = BLANK : [*map(int,inp().split(x))]
mfi = lambda x = BLANK : [*map(float,inp().split(x))]
ii = lambda : int(inp())
fi = lambda : float(inp())
p = print
def solve():
while 1:
n = ii()
if n == 0:
break
cnt = 0
for a in range(1, n):
# b^2 + b = k
k = 2 * n - a + a * a
b = a + 1
while b < n and b * b + b <= k:
if b * b + b == k:
cnt += 1
b += 1
p(cnt)
if __name__ == "__main__":
tc = 1
for t in range(1, tc+1):
ret = solve()