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Finding Mino

You have been given a Unimodal function: f(x) = 2x^2 - 12x + 7 with N intervals. For each interval, you will be given two integer values l and r, where and you need to find the minimum value of f(x) where x will be in the range [l, r] (both inclusive).

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Finding Mino

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You have been given a Unimodal function: f(x) = 2x^2 - 12x + 7 with N intervals. For each interval, you will be given two integer values l and r, where and you need to find the minimum value of f(x) where x will be in the range [l, r] (both inclusive).

Constraints

1 <= N <= 10^5 -10^6 <= l <= r <= 10^6

Format

Input

The first line will consist of one integer N denoting the number of intervals. In the next N lines, each line contains 2 space-separated integers, l, and r denoting the range of interval.

Output

Print N lines, where ith line denotes the minimum value of f(x), where x will be in the range [li, ri];

Example

Sample Input

1 6 8

Sample Output

7

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