Description

Fibonacci numbers are well-known as follow:
Now given an integer $N$, please find out whether $N$ 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 $T (T \leq 10000)$, indicating the number of test cases.

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

Output

One line per case.
If the answer don’t exist, output “-1” (without quotes).
Otherwise, your answer should be formatted as “$N=f_1+f_2+…+f_n$”.
$N$ indicates the given number and $f_1, f_2, … , f_n$ 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