In mathematics the Fibonacci series or Fibonacci sequence are the numbers in the following integer sequence.

0, 1, 1, 2, 3, 5, 8, 13, 21 ... By definition, the first two numbers in the Fibonacci sequence are 0 and 1, and each subsequent number is the sum of the previous two.

In mathematical terms, the sequence F_n of Fibonacci numbers is defined by the recurrence relation:

F_n = F_n-1 + F_n-2

Your task is to divide given Fibonacci number n into three different Fibonacci numbers (a, b, c) (without zero) or say that it is impossible.

Input

Input starts with an integer T (T <= 1000), denoting the number of test cases. Each case starts with an integer n (0 <= n < 10¹²). It is guaranteed that n is a Fibonacci number.

Output

Print three required numbers: a, b and c (a < b < c) (without zero). a, b, c must be Fibonacci number and the total sum of a, b, c equal to n. If there is no answer for the test you have to print "impossible" (without the quotes).

Example

Input:
1
8

Output:
1 2 5

Problem setter: Shipu Ahamed, Dept. of CSE
Bangladesh University of Business and Technology (BUBT)