Given a large number N, write a program to count the ways to break it into three whole numbers such that they sum up to the original number.
Example 1:
Input: N = 3
Output: 10
Explaination: The ways are 
0 + 0 + 3 = 3
0 + 3 + 0 = 3
3 + 0 + 0 = 3
0 + 1 + 2 = 3
0 + 2 + 1 = 3
1 + 0 + 2 = 3
1 + 2 + 0 = 3
2 + 0 + 1 = 3
2 + 1 + 0 = 3
1 + 1 + 1 = 3
Example 2:
Input: N = 1
Output: 3
Explaination: The ways are:
1 + 0 + 0 = 1
0 + 1 + 0 = 1
0 + 0 + 1 = 1
Your Task:
You do not need to read input or print anything. Your task is to complete the function countWays() which takes N as input parameter and returns the total number of possible ways to break N in three whole numbers.
Expected Time Complexity: O(1)
Expected Auxiliary Space: O(1)
Constraints:
1 ≤ N ≤ 10^{9}

Source: geeksforgeeks | Difficulty: EASY
Tags: Mathematics

Starter code: #User function Template for python3

class Solution:
    def countWays(self, N):
        # code here

Solutions:
class Solution:

	def countWays(self, N):
		return N * (N + 1) // 2 + (N + 1)


class Solution:

	def countWays(self, n):
		c = 0
		c = (n + 1) * (n + 2) // 2
		return c


class Solution:

	def countWays(self, N):
		return (N + 2) * (N + 1) // 2
if __name__ == '__main__':
	t = int(input())
	for _ in range(t):
		N = int(input())
		ob = Solution()
		print(ob.countWays(N))


class Solution:

	def countWays(self, N):
		a = int((N + 2) * (N + 1) / 2)
		return a


class Solution:

	def countWays(self, n):
		return (n + 2) * (n + 1) // 2


class Solution:

	def countWays(self, N):
		ways = int((N + 2) * (N + 1) / 2)
		return ways


from itertools import permutations

class Solution:

	def countWays(self, N):
		return (N + 2) * (N + 1) // 2


class Solution:

	def countWays(self, N):
		l = (N + 2) * (N + 1) / 2
		l = int(l)
		return l


class Solution:

	def countWays(self, N):
		a = N + 2
		k = 2
		return a * (a - 1) // 2


class Solution:

	def countWays(self, N):
		count = 0
		count = (N + 1) * (N + 2) // 2
		return count


class Solution:

	def countWays(self, n):
		j = n * (n + 1) / 2
		return int(j + n + 1)


class Solution:

	def countWays(self, N):
		cout = 0
		cout = (N + 1) * (N + 2) // 2
		return cout


class Solution:

	def countWays(self, n):
		count = 0
		count = (n + 1) * (n + 2) // 2
		return count


import math

class Solution:

	def countWays(self, N):
		fac = (N + 2) * (N + 1)
		ans = fac // 2
		return ans


class Solution:

	def countWays(self, N):
		if N == 0:
			return 1
		else:
			count = int((N + 2) * (N + 1) / 2)
		return count


class Solution:

	def countWays(self, N):
		count = int((N + 1) * (N + 2) / 2)
		return count


import itertools

class Solution:

	def countWays(self, N):
		return (N + 2) * (N + 1) // 2