Score : 700 points
10^{10^{10}} participants, including Takahashi, competed in two programming contests. In each contest, all participants had distinct ranks from first through 10^{10^{10}}-th.
The score of a participant is the product of his/her ranks in the two contests.
Process the following Q queries:
Input is given from Standard Input in the following format:
Q A_1 B_1 : A_Q B_Q
For each query, print the maximum possible number of participants whose scores are smaller than Takahashi's.
8 1 4 10 5 3 3 4 11 8 9 22 40 8 36 314159265 358979323
1 12 4 11 14 57 31 671644785
Let us denote a participant who was ranked x-th in the first contest and y-th in the second contest as (x,y).
In the first query, (2,1) is a possible candidate of a participant whose score is smaller than Takahashi's. There are never two or more participants whose scores are smaller than Takahashi's, so we should print 1.