Write a program which, given an integer $n$ as input, will produce a
mathematical expression whose solution is $n$. The solution is restricted to
using exactly four $4$’s
and exactly three of the binary operations selected from the
set $\{ *, +, , /\} $.
The number $4$ is the ONLY
number you can use. You are not allowed to concatenate fours to
generate other numbers, such as $44$ or $444$.
For example given $n=0$, a solution is $4 * 4  4 * 4 = 0$. Given
$n=7$, a solution is
$4 + 4  4~ /~ 4 = 7$.
Division is considered truncating integer division, so that
$1/4$ is $0$ (instead of $0.25$). Assume the usual precedence
of operations so that $4 + 4 * 4
= 20$, not $32$.
Not all integer inputs have solutions using four $4$’s with the aforementioned
restrictions (consider $n=11$).
Hint: Using your forehead and some forethought should
make an answer forthcoming. When in doubt use the
fourth.
Input
Input begins with an integer $1 \leq m \leq 1\, 000$, indicating
the number of test cases that follow. Each of the next
$m$ lines contain exactly
one integer value for $n$
in the range $1\, 000\, 000 \leq
n \leq 1\, 000\, 000$.
Output
For each test case print one line of output containing
either an equation using four $4$’s to reach the target number or
the phrase no solution. Print the equation
following the format of the sample output; use spaces to
separate the numbers and symbols printed. If there is more than
one such equation which evaluates to the target integer, print
any one of them.
Sample Input 1 
Sample Output 1 
5
9
0
7
11
24

4 + 4 + 4 / 4 = 9
4 * 4  4 * 4 = 0
4 + 4  4 / 4 = 7
no solution
4 * 4 + 4 + 4 = 24
