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 B {

    static int lowerBound(ArrayList<Long> al, int val) {
        int start = 0;
        int end = al.size() - 1;

        int ans = 0;

        while (start <= end) {
            int mid = (start + end) / 2;

            if (al.get(mid) < val) {
                ans = mid;
                start = mid + 1;
            } else {
                end = mid - 1;
            }
        }

        return ans;

    }

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        StringBuilder sb = new StringBuilder();
        int testCases = sc.nextInt();

        ArrayList<Long> al = new ArrayList<>();

        long pow = 3;
        while ((pow * pow) / 2 <= 1e9) {
            al.add((pow * pow) / 2);
            pow = pow + 2;
        }

        // System.out.println(al.get(al.size() - 1));

        for (int t = 0; t < testCases; t++) {
            int n = sc.nextInt();

            if (n <= 4) {
                sb.append("0").append("\n");
                continue;
            }

            int ans = lowerBound(al, n) + 1;

            sb.append(ans).append("\n");

        }

        System.out.print(sb);
    }
}