Implement Numerically Stable Softmax

Problem: Implement Numerically Stable Softmax Given a floating-point array x of length n, implement softmax: [ \operatorname{softmax}(x_i) = \frac{e^{x_i}}{\sum_{j=1}^{n} e^{x_j}} ] Print the softmax probability for every element, rounded to 6 decimal places. The input may contain large values. Your implementation must be numerically stable and must not overflow when computing exponentials. Input Format First line: integer n Second line: n floating-point values x_1, x_2, ..., x_n Output Format Print n softmax values separated by spaces, each rounded to 6 decimal places. Constraints 1 <= n <= 10^5 -10^4 <= x_i <= 10^4 Example Input 3 1 2 3 Output 0.090031 0.244728 0.665241 Example Input 3 1 2 3 Output 0.090031 0.244728 0.665241