Your task is to compute natural logarithm of the absolute value of the Bernoulli number for many integer parameters N.

I/O format is the same as in BINARYIO.

Input

Array of unsigned 32 bit integers in binary format (use fread in C/C++)

To read unsigned N use fread(&N, sizeof(N), 1, stdin)  instead of usual scanf("%u", &N) until the end of file.

For each test case 2 ≤ N < 2³², N is even. There will be up to 1,250,000 numbers in input file.

Output

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

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

For each N output ln(|B_N|) with absolute or relative error less than 10^-15

Example

Input:

4

10

50

Output:

-3,4011973816621553754132366916069

-2,580216829592325170273661603119

57,277060811865704087099873424857

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

TL = 5 * My time