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.io.*;
import java.util.Arrays;
import java.util.StringTokenizer;

public class D {

    public void solve() {
        int t = in.nextInt();


        while (t-- > 0) {
            int n = in.nextInt();

            long step = 2;
            long b = 1;
            int ans = 0;
            for (long a = 3; a <= n && b*4<=n; a += 2) {
                long c = a*a - b*4;
                if (c > n) break;
                if (a <= b*4 && 4*b <= c && c <= n) ans++;
                b += step;
                step++;
            }

            out.println(ans);
        }
    }

    String input = "";
    String output = "";
    FastScanner in;
    PrintWriter out;

    void run() throws Exception {
        if (input.length() == 0) {
            in = new FastScanner(System.in);
        } else {
            in = new FastScanner(new File(input));
        }
        if (output.length() == 0) {
            out = new PrintWriter(System.out);
        } else {
            out = new PrintWriter(new File(output));
        }

        solve();

        out.close();

    }

    public static void main(String[] args) throws Exception {
        new D().run();
    }

    class FastScanner {

        BufferedReader bf;
        StringTokenizer st;

        public FastScanner(InputStream is) {
            bf = new BufferedReader(new InputStreamReader(is));
        }

        public FastScanner(File fr) throws FileNotFoundException {
            bf = new BufferedReader(new FileReader(fr));
        }

        public String next() {
            try {
                while (st == null || !st.hasMoreTokens()) {
                    st = new StringTokenizer(bf.readLine());
                }
            } catch (IOException ex) {
                ex.printStackTrace();
            }
            return st.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

        public long nextLong() {
            return Long.parseLong(next());
        }

        public double nextDouble() {
            return Double.parseDouble(next());
        }

        public int[] readIntArray(int length) {
            int arr[] = new int[length];
            for (int i = 0; i<length; i++)
                arr[i] = nextInt();
            return arr;
        }
    }
}