During excavations in the Dreisamwuste, a desert on some far away and probably uncivilized planet, sheets of paper containing mysterious symbols had been found. After a long investigation, the project scientists have concluded that the symbols might be parts of equations. If this were true, it would be proof that the Dreisamwuste was civilized a long long time ago.
The problem, however, is that the only symbols found on the sheets are digits, parantheses and equality signs. There is strong evidence that the people living in the Dreisamwuste knew only of three arithmetic operations: addition, subtraction, and multiplication. It is also known that the people of the Dreisamwuste did not have prioritization rules for arithmetic operations - they evaluate all terms strictly left to right. For example, for them the term 3 + 3 * 5 would be equal to 30, and not 18.
But currently, the sheets do not contain any arithmetic operators. So if the hypothesis is true, and the numbers on the sheets form equations, then the operators must have faded away over time.
You are the computer expert who is supposed to find out whether the hypothesis is sensible or not. For some given equations (without arithmetic operators) you must find out if there is a possibility to place +, -, and * in the expression, so that it yields a valid equation. For example, on one sheet, the string "18=7 (5 3) 2" has been discovered. Here, one possible solution is "18=7+(5-3)*2". But if there was a sheet containing "5=3 3", then this would mean that the Dreisamwuste people did not mean an equation when writing this.
18 = 7 (5 3) 2 30 = 3 3 5 18 = 3 3 5 5 = 3 3 0
Equation #1: 18=7+(5-3)*2 Equation #2: 30=3+3*5 Equation #3: Impossible. Equation #4: Impossible.