CF1487D.Pythagorean Triples

A 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.

毕达哥拉斯三元组是指满足以下条件的三个整数 $(a, b, c)$：以 $a$、$b$ 和 $c$ 分别作为两条直角边与斜边的长度，可以构成一个直角三角形。一个毕达哥拉斯三元组的例子是 $(3, 4, 5)$。

瓦夏正在研究直角三角形的性质，他使用一个公式来判断某组整数是否构成毕达哥拉斯三元组。不幸的是，他忘记了该公式的准确形式；他只记得这个公式是一个包含平方项的等式。于是，他提出了如下公式：$c = a^2 - b$。

显然，该公式并不能正确判定一个三元组是否为毕达哥拉斯三元组。但令瓦夏惊讶的是，它对三元组 $(3, 4, 5)$ 却恰好成立：$5 = 3^2 - 4$，因此根据瓦夏的公式，$(3, 4, 5)$ 被判定为毕达哥拉斯三元组。

当瓦夏最终找到了正确的公式（并意识到自己提出的公式是错误的）后，他开始思考：在满足 $1 \le a \le b \le c \le n$ 的所有整数三元组 $(a, b, c)$ 中，有多少个三元组同时满足瓦夏的公式和毕达哥拉斯三元组的真实定义？他请你计算这样的三元组的个数。

The 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 $n$ ($1 \le n \le 10^9$).

第一行包含一个整数 $t$（$1 \le t \le 10^4$）—— 测试用例的数量。

每个测试用例由一行组成，该行包含一个整数 $n$（$1 \le n \le 10^9$）。

For 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.

对于每个测试用例，输出一个整数——满足 $1 \le a \le b \le c \le n$ 的整数三元组 $(a, b, c)$ 的个数，使得该三元组既符合勾股定理的真实定义，又符合瓦夏提出的公式。

The 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 $1$.

唯一满足 $c = a^2 - b$ 且 $1 \le a \le b \le c \le 9$ 的毕达哥拉斯三元组是 $(3, 4, 5)$；因此，当 $n = 3$ 时答案为 $0$，而当 $n = 6$（以及 $n = 9$）时答案为 $1$。