Finding a Special Combination

Given a positive integer N, find a combination of three pairs of integers \((a, b)\), \((c, d)\) and \((e, f)\) satisfying the equation

[ a + b^2 + c + d^2 + e + f^2 = N ]

with the additional constraints:

• \(1 \le a, b, c, d, e, f \le 10^6\)

If there are multiple solutions, you may output any valid one. It is guaranteed that for the given input values there exists at least one valid solution.

Note: In this problem, you are required to read the input from standard input and write the output to standard output. The output should contain the 6 integers \(a, b, c, d, e, f\) separated by a single space.

Examples:

• For input 53, one possible valid output is 1 5 1 4 1 3 since \[ 1 + 5^2 + 1 + 4^2 + 1 + 3^2 = 1 + 25 + 1 + 16 + 1 + 9 = 53 \]
• For input 220, one possible valid output is 1 12 1 8 1 3 since \[ 1 + 12^2 + 1 + 8^2 + 1 + 3^2 = 1 + 144 + 1 + 64 + 1 + 9 = 220 \]
• For input 1000, one possible valid output is 1 30 1 9 1 4 since \[ 1 + 30^2 + 1 + 9^2 + 1 + 4^2 = 1 + 900 + 1 + 81 + 1 + 16 = 1000 \]

inputFormat

The input is a single positive integer N read from standard input.

Format:

N

outputFormat

Output 6 integers \(a, b, c, d, e, f\) separated by a single space on one line such that they satisfy

[ a + b^2 + c + d^2 + e + f^2 = N ]

and the constraints \(1 \le a, b, c, d, e, f \le 10^6\).

## sample

53

1 5 1 4 1 3