Find all pairs of numbers $$x, y \in \mathbb{N}$$ of which the sum equals a given number $$n \in \mathbb{N}$$, and of which $$y$$ can be achieved by removing one of the numbers of $$x$$. The number $$x$$ must have two digits, of which the first cannot be zero. The number $$y$$ thus always has one less digit than $$x$$ and can start with zero.

Input

The first line of the input contains a natural number $$t$$ ($$1 \leq t \leq 100$$) that indicates how many test cases there are. The following $$t$$ lines each contain one integer $$n$$ ($$10 \leq n \leq 10^4$$).

Output

For each test case, a number must be issued indicating how many pairs of numbers exist that meet the problem description for the given number $$n$$. Then, the different sets of numbers $$(x,y)$$ are written out. Each pair is written on a separate line, in ascending order of the value $$x$$. The pairs are written in the following format: \[x + y = n\] $$x$$, $$y$$ and $$n$$ are to be replaced by the corresponding numbers, and there must be a single space on either side of the plus sign (+) and the equality sign (=).

Example

Input:

2
302
11

Output:

5
251 + 51 = 302
275 + 27 = 302
276 + 26 = 302
281 + 21 = 302
301 + 01 = 302
1
10 + 1 = 11