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:
//WHEN IN DOUBT , USE BRUTE FORCE !!!!!!!!!
import java.lang.String;
import java.io.*;
import java.util.*;
import java.util.StringTokenizer;
//class Main    //AtCoder()
//class Solution // Codechef
public class Solution2 //Codeforces
{
    public static void main(String args[])
    {
        try {
            FastReader sc = new FastReader();
            int TT = sc.nextInt();
            for(int hehe=1 ; hehe  <= TT ; hehe++){
                long N= sc.nextLong(),cnt=0;
                //long sqrt=2*(long)Math.sqrt(N) + 2,cnt=0;
                for(int i=3;i*i<=2*N - 1;i+=2){
                    cnt++;
                }

                sopln(cnt);
            }
            out.flush();
        }catch (Exception e) {
            sopln(e.toString());
        }
    }
    public final static int d = 256;
    static int MOD = 1000000007;
    static final double PI = Math.PI;
    private static BufferedReader in = new BufferedReader (new InputStreamReader (System.in));
    private static PrintWriter out = new PrintWriter (new OutputStreamWriter (System.out));
    static 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());}char nextChar(){try {return (char) (br.read());}catch (IOException e){return '~';}}double nextDouble(){return Double.parseDouble(next());}
        String nextLine(){String str = "";try{str = br.readLine();}catch (IOException e){e.printStackTrace();}return str;}
    }
    static void sop(Object o){out.print(o);}
    static double ceil(double d){
        return Math.ceil(d);
    }
    static double floor(double d){
        return Math.floor(d);
    }
    static double round(double d){
        return Math.round(d);
    }
    static void sopln(Object o){out.println(o);}
    static void printArray(int[] arr){
        for(int i=0;i<arr.length;i++){
            sop(arr[i]+" ");
        }
        sopln("");
    }
}