Given an integer n, you have to find whether it can be expressed as summation of factorials. For given n, you have to report a solution such that

n = x₁! + x₂! + ... + x_n! (x_i < x_j for all i < j)

Input

Input starts with an integer T (≤ 10000), denoting the number of test cases.

Each case starts with a line containing an integer n (1 ≤ n ≤ 10¹⁸

Output

For each case, print the case number and the solution in summation of factorial form. If there is no solution then print'impossible'. There can be multiple solutions, any valid one will do. See the samples for exact formatting.

Note

Be careful about the output format; you may get wrong answer for wrong output format.

題意：N如果可以表示成某幾個數的階乘則找出這幾個數，不能的話輸出impossible,不能有x相同的的數;