## PYTRIP2 - Pythagorean triples (medium)

Pythagoras is credited, by tradition, for the first proof of the relation a2 + b2 = c2 in any right angled triangle where c is hypotenuse and a and b are the catheti.

We define a Pythagorean triple as a set of three positive integers a, b, and c which satisfy the above equation , ie , a2 + b2 = c2.
{3,4,5} is the most common example of such triples.

### Input

The first line of input contains an integer T, the number of test cases.

Each of the next T lines contains two integers N, M.

### Output

For each test case, print on a single line the number of Pythagorean triplet {a,b,c} such that N ≤ a,b,c ≤ M.

### Example

```Input:
3
1 5
4 10
10 100

Output:
1
1
45
```

### Constraints

```0 < T < 100
0 < N < M
0 < T × M < 1.21×10^8
```

There are several input files.
Time limit is ×20 my top speed with C language (1kB of code).
For your information, my total best time is 0.59s for the 6 input files. (Edit 2017-02-11, after compiler changes).
Warning, it could be hard with interpreted languages.
You can try before the quite similar tutorial problem : PYTRIP before.

### Information

This problem is part of the Bubble Cup competition qualification round (April 2014).
@students: good luck. GNU_salutations.