Diagonal

The number of diagonals of an $n$-gon is not less than $N$. What is the minimum possible value of $n$?

Input

Contains less than $1001$ lines. Each line contains a positive integer $N(N\le 10^{15})$ that indicates the minimum possible number of diagonals. Input is terminated by a line with one $0$ that should not be processed.

Output

For each test case produce one line that contains serial number and the minimum possible value for $n$ (number of sides).

Examples