#SDNU1504. B.Fibonacci

B.Fibonacci

Description

Fibonacci numbers are well-known as follow:
Now given an integer NN, please find out whether NN can be represented as the sum of several Fibonacci numbers in such a way that the sum does not include any two consecutive Fibonacci numbers.

Format

Input

Multiple test cases, the first line is an integer T(T10000)T (T \leq 10000), indicating the number of test cases.

Each test case is a line with an integer N(1N1000000000)N (1\leq N \leq 1000000000).

Output

One line per case.
If the answer don’t exist, output “-1” (without quotes).
Otherwise, your answer should be formatted as “N=f1+f2++fnN=f_1+f_2+…+f_n”.
NN indicates the given number and f1,f2,,fnf_1, f_2, … , f_n indicating the Fibonacci numbers in ascending order.
If there are multiple ways, you can output any of them.

Samples

4
5
6
7
100
5=5
6=1+5
7=2+5
100=3+8+89