Linear Equation

For each linear equation ax + b = c, decide whether it has no, one, or infinitely many solutions and print the root truncated to six decimals.

Easy2MathImplementationNo attempts yetTime limit2sMemory limit512 MB

Problem

Write a program that solves a simple linear equation.

Input

The first line contains an integer PP (1P1001 \le P \le 100), the number of data sets. Each of the next PP lines contains one linear equation. Every equation consists of ax, a single space, the sign +, a single space, b, a single space, the sign =, a single space, and c, in that order:

ax + b = c

Here xx is the variable, and aa, bb, cc are non-negative integers (0a,b,c1090 \le a, b, c \le 10^9). The coefficient aa is always written as a number, even when it is 00 or 11.

Output

For each data set, print two lines. The first line is Equation n, where nn is the number of the data set, starting from 1. The second line is the answer:

  • If the equation has no solution, print No solution..
  • If the equation has infinitely many solutions, print More than one solution..
  • If the equation has exactly one solution, print x = followed by the solution truncated to six digits after the decimal point. Truncation is toward zero: drop every digit of the absolute value after the sixth decimal place, then put - in front if the solution is negative. If the truncated value is 00, print x = 0.000000 with no sign. Always print exactly six digits after the decimal point.

Print a blank line after the output of each data set.