List Comprehensions

 Let's learn about list comprehensions! You are given three integers  and  representing the dimensions of a cuboid along with an integer . Print a list of all possible coordinates given by  on a 3D grid where the sum of  is not equal to . Here, . Please use list comprehensions rather than multiple loops, as a learning exercise.

Example



All permutations of  are:
.

Print an array of the elements that do not sum to .

Input Format

Four integers  and , each on a separate line.

Constraints

Print the list in lexicographic increasing order.

Sample Input 0

1
1
1
2

Sample Output 0

[[0, 0, 0], [0, 0, 1], [0, 1, 0], [1, 0, 0], [1, 1, 1]]

Explanation 0

Each variable  and  will have values of  or . All permutations of lists in the form .
Remove all arrays that sum to  to leave only the valid permutations.

Sample Input 1

2
2
2
2

Sample Output 1

[[0, 0, 0], [0, 0, 1], [0, 1, 0], [0, 1, 2], [0, 2, 1], [0, 2, 2], [1, 0, 0], [1, 0, 2], [1, 1, 1], [1, 1, 2], [1, 2, 0], [1, 2, 1], [1, 2, 2], [2, 0, 1], [2, 0, 2], [2, 1, 0], [2, 1, 1], [2, 1, 2], [2, 2, 0], [2, 2, 1], [2, 2, 2]]

if __name__ == '__main__':
    x = int(input())
    y = int(input())
    z = int(input())
    n = int(input())
    
    res=[[i,j,k] for i in range(x+1) for j in range(y+1) for k in range (z+1) if (i+j+k)!=n]
    # res=[]
    # for i in range(x+1):
    #     for j in range(y+1):
    #         for k in range(z+1):
                
    #             if (i+j+k)!=n:
    #                 res.append([i,j,k])
                
    print(res)

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