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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.Arrays;
import java.util.Random;
import java.util.StringTokenizer;

//Good morning!
public class D {

    public static void main(String[] args) {
        FastScanner fs=new FastScanner();
        int T=fs.nextInt();
        for (int tt=0; tt<T; tt++) {
            int n = fs.nextInt();
//            int ans = ((int) Math.sqrt(2*n - 1) - 1) / 2;
//            System.out.println(ans);
            int ans = 0;
            for (int i = 3; i <= Math.sqrt(2*n - 1); i = i + 2) {
                ans++;
            }
            System.out.println(ans);
        }
    }

    // Use this instead of Arrays.sort() on an array of ints. Arrays.sort() is n^2
    // worst case since it uses a version of quicksort. Although this would never
    // actually show up in the real world, in codeforces, people can hack, so
    // this is needed.
    static void ruffleSort(int[] a) {
        //ruffle
        int n=a.length;
        Random r=new Random();
        for (int i=0; i<a.length; i++) {
            int oi=r.nextInt(n), temp=a[i];
            a[i]=a[oi];
            a[oi]=temp;
        }

        //then sort
        Arrays.sort(a);
    }

    // Use this to input code since it is faster than a Scanner
    static class FastScanner {
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st=new StringTokenizer("");
        String next() {
            while (!st.hasMoreTokens())
                try {
                    st=new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }
        int[] readArray(int n) {
            int[] a=new int[n];
            for (int i=0; i<n; i++) a[i]=nextInt();
            return a;
        }
        long nextLong() {
            return Long.parseLong(next());
        }
    }
}