Your task is to compute natural logarithm for real parameter X with absolute or relative error less than 10^-12.

Input

Array of doubles in binary format (use fread in C/C++)

10^-12 ≤ X ≤ 10¹². There will be up to 1,000,000 numbers in array.

Output

Array of doubles in binary format (use fwrite in C/C++)

For each number in input you should output the corresponding answer.

Example

Input:
1
10

Output:
0
2.3025850929940456840179914546844

Note: Sample input and output are readable for your convenience!!!

Arrays in memory and in input are byte-to-byte identical.

To read double a use fread(&a, sizeof(a), 1, stdin) instead of scanf("%lf", &a) until the end of file.

To write double a use fwrite(&a, sizeof(a), 1, stdout) instead of printf("%lf\n", a).