PAIRINT - Pairs of Integers

no tags 

You are to find all pairs of integers such that their sum is equal to the given integer number N and the second number results from the first one by striking out one of its digits. The first integer always has at least two digits and starts with a non-zero digit. The second integer always has one digit less than the first integer and may start with a zero digit.

Input

The first line of the input file is the integer number t ( 1 ≤ t ≤ 20 ), the number of test cases. Then t lines follow, each test case in one line; the line consists of a single integer N (10 ≤ N ≤ 10^9).

Output

For each test case:

On the first line write the total number of different pairs of integers that satisfy the problem statement. On the following lines write all those pairs. Write one pair on a line in ascending order of the first integer in the pair. Each pair must be written in the following format

X + Y = N

Here X, Y, and N, must be replaced with the corresponding integer numbers. There should be exactly one space on both sides of '+' and '=' characters.

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

hide comments
phucdtd: 2015-11-22 13:13:33

0.127 giây... 100% t bị TLE T-T

Varun Rajeev: 2014-12-17 13:17:53

250 + 52 also solution?


Added by:Nguyen Minh Hieu
Date:2006-01-01
Time limit:0.127s
Source limit:10000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:ADA95 ASM32 BASH BF C CSHARP CPP CLPS LISP sbcl LISP clisp D FORTRAN HASK ICON ICK JAVA LUA NEM NICE OCAML PAS-GPC PAS-FPC PERL PHP PIKE PRLG-swi PYTHON RUBY SCM qobi SCM guile ST TEXT WHITESPACE
Resource:2001-2002 ACM Northeastern European Regional Programming Contest