# Sliding window

class Solution(object):

def consecutiveNumbersSum(self, N):

i = 1

j = 2

s = 1 #sum(range(i, j))

ans = 0

while i<=j and j<=N+1:

if s==N:

ans += 1

s += j

j += 1

elif s>N:

s -= i

i += 1

else:

s += j

j += 1

return ans

#Math

class Solution(object):

def consecutiveNumbersSum(self, N):

ans = 0

upperLimit = int((2 * N + 0.25)**0.5 - 0.5) + 2

for x in xrange(1, upperLimit):

if x%2==0:

if float(N)/x-N/x==0.5:

upper = N/x + x/2

lower = N/x - x/2 + 1

if 1<=lower and upper<=N:

ans += 1

else:

if N%x==0:

upper = N/x + (x-1)/2

lower = N/x - (x-1)/2

if 1<=lower and upper<=N:

ans += 1

return ans