Problem: 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 ≤ a ≤ b ≤ c ≤ n such that they are Pythagorean both according to his formula and the real definition? He asked you to count these triples.

Input

The first line contains one integer t (1 ≤ t ≤ 10^4) — the number of test cases.

Each test case consists of one line containing one integer n (1 ≤ n ≤ 10^9).

Output

For each test case, print one integer — the number of triples of integers (a, b, c) with 1 ≤ a ≤ b ≤ c ≤ n such that they are Pythagorean according both to the real definition and to the formula Vasya came up with.

Example

Input


3
3
6
9


Output


0
1
1

Note

The only Pythagorean triple satisfying c = a^2 - b with 1 ≤ a ≤ b ≤ c ≤ 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.

Solution (in JAVA):

Solution:
import java.util.*;
public class PythagoreanTriples {
    public static void main(String[] args) {
        List<Integer> list = new ArrayList<>();
        int i = 3;
        while (true) {
            int j = i * i / 2;
            int k = j + 1;
            if (k >= 1000000000) {
                break;
            }
            list.add(k);
            i += 2;
        }
        Collections.sort(list);
        Scanner in = new Scanner(System.in);
        int T = in.nextInt();
        for (int t = 0; t < T; t++) {
            int N = in.nextInt();
            System.out.println(Math.max(search(list, 0, list.size(), N), 0));
        }
    }
    public static int search(List<Integer> list, int l, int r, int n) {
        if (l >= r) {
            return -1;
        }
        int mid = (l + r) / 2;
        if (list.get(mid) <= n) {
            int m = search(list, mid + 1, r, n);
            if (m != -1) {
                return m;
            }
            return mid + 1;
        }
        return search(list, l, mid, n);
    }
}