When I [ Run & Check] following code, it's hanged up but Why?

def checkio(number):
    remain = number
    pigeons = {}
    offset = 0
    count = 0

    for i in range(number):
        offset += count
        count += 1
        for j in range(count):
            pigeons[offset + j] = 0
        for k in pigeons:
            if remain > 0:
                pigeons[k] += 1
                remain -= 1

    result = 0
    for k in pigeons:
        if pigeons[k] > 0:
            result += 1

    return result

#These "asserts" using only for self-checking and not necessary for auto-testing
if __name__ == '__main__':
    assert checkio(1) == 1, "1st example"
    assert checkio(2) == 1, "2nd example"
    assert checkio(5) == 3, "3rd example"
    assert checkio(10) == 6, "4th example"