D. Pythagorean Triplestime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputA Pythagorean triple is a triple of integer numbers (a, b, c) such that it is possible to form a right triangle with the lengths of the first cathetus, the second cathetus and the hypotenuse equal to a, b and c, respectively. An example of the Pythagorean triple is (3, 4, 5).Vasya studies the properties of right triangles, and he uses a formula that determines if some triple of integers is Pythagorean. Unfortunately, he has forgotten the exact formula; he remembers only that the formula was some equation with squares. So, he came up with the following formula: c = a^2 - b.Obviously, this is not the right formula to check if a triple of numbers is Pythagorean. But, to Vasya's surprise, it actually worked on the triple (3, 4, 5): 5 = 3^2 - 4, so, according to Vasya's formula, it is a Pythagorean triple.When Vasya found the right formula (and understood that his formula is wrong), he wondered: how many are there triples of integers (a, b, c) with 1 \le a \le b \le c \le n such that they are Pythagorean both according to his formula and the real definition? He asked you to count these triples.InputThe first line contains one integer t (1 \le t \le 10^4) — the number of test cases.Each test case consists of one line containing one integer n (1 \le n \le 10^9).OutputFor each test case, print one integer — the number of triples of integers (a, b, c) with 1 \le a \le b \le c \le n such that they are Pythagorean according both to the real definition and to the formula Vasya came up with.ExampleInput
3
3
6
9
Output
0
1
1
NoteThe only Pythagorean triple satisfying c = a^2 - b with 1 \le a \le b \le c \le 9 is (3, 4, 5); that's why the answer for n = 3 is 0, and the answer for n = 6 (and for n = 9) is 1.
3
3
6
9

0 1 1 
['binary search', 'brute force', 'math', 'number theory', '*1500']