Utkarsh is going to Cherrapunji to visit his brother Saharsh. Cherrapunji faces one of largest rainfall in the country. So, Saharsh and Utkarsh decided to measure this rainfall by T Rain Gauges. They were going to measure it by taking the product of the readings of all the gauges. But, they found out that the gauges were not working properly and were producing random values. The brothers want to know what will be the expected result of the experiment.

The i^th Rain Gauge has a least count of 1/R_i units. It has N_i divisions on its surface. Formally, it can give any reading from the set {0, 1/R_i , 2/R_i , ... ,N_i/R_i}. It gives a reading x with a probability proportional to x².

Input Format:
The first line contains the integer T. T lines follow each containing 2 integers - N_i and R_i.

Output format:
Print the answer to the problem as real number exactly 4 decimal places. It is guaranteed that the answer is always less than 10⁹.

Constraints:
1 ≤ T ≤ 10³
1 ≤ N_i ≤ 10³
1 ≤ R_i ≤ 10³

NOTE:

A function p(x) is said to be proportional to x² means p(x) = ax² for some non negative a.

All the rain gauges produce values independently from each other.