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:
//whenever you are not able to understand the before and after thingy, use the concept of cycles and memoisation.
import java.io.BufferedReader;
import java.io.InputStream;
import java.util.*;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.StringTokenizer;


public class Main {
    //    static Integer[][] tokens;
    static int n;

    public static void main(String[] args) throws IOException {
        FastReader reader = new FastReader();
        int test = reader.nextInt();

        for (int o = 0; o < test; o++) {
            int n = reader.nextInt();
            int ans = 0;
            for (int i = 3; i * i <= 2 * n - 1; i += 2)
                ++ans;
            System.out.println(ans);

            }

        }
    }

class Node {
    long demand = 0;
    long day = 0; long sadness = 0; boolean f = false;
    public Node(long day, long demand, long sadness){
        this.demand = demand;
        this.day = day;
        this.sadness = sadness;
    }
}








class FastReader
{
    BufferedReader br;
    StringTokenizer st;

    public FastReader()
    {
        br = new BufferedReader(new
                InputStreamReader(System.in));
    }

    String next()
    {
        while (st == null || !st.hasMoreElements())
        {
            try
            {
                st = new StringTokenizer(br.readLine());
            }
            catch (IOException  e)
            {
                e.printStackTrace();
            }
        }
        return st.nextToken();
    }

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

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

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

    String nextLine()
    {
        String str = "";
        try
        {
            str = br.readLine();
        }
        catch (IOException e)
        {
            e.printStackTrace();
        }
        return str;
    }
}

/** Class for buffered reading int and double values */
class Reader {
    static BufferedReader reader;
    static StringTokenizer tokenizer;

    /** call this method to initialize reader for InputStream */
    static void init(InputStream input) {
        reader = new BufferedReader(
                new InputStreamReader(input) );
        tokenizer = new StringTokenizer("");
    }

    /** get next word */
    static String next() throws IOException {
        while ( ! tokenizer.hasMoreTokens() ) {
            //TODO add check for eof if necessary
            tokenizer = new StringTokenizer(
                    reader.readLine() );
        }
        return tokenizer.nextToken();
    }

    static int nextInt() throws IOException {
        return Integer.parseInt( next() );
    }

    static double nextDouble() throws IOException {
        return Double.parseDouble( next() );
    }
}