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:
//package com.tarun.GR13;

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

public class D {
    public static void main(String[] args) {
        FastScanner fs = new FastScanner();
        int t = fs.nextInt();
        while(t-- > 0){
             long n = fs.nextLong(),ans=0;
             for(long a =3; a*a <= 2*n-1 ; a+=2){
//                 long aSquare = a*a;
//                 long b = (aSquare - 1)/2;
//                 long cSquare = aSquare + b*b;
                 ans++;
//                 System.out.println((a*a)+" "+(b*b)+" "+cSquare);
             }
            System.out.println(ans);
        }
    }
    static class FastScanner {
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st=new StringTokenizer("");
        public String next(){
            while(!st.hasMoreTokens()){
                try{
                    st=new StringTokenizer(br.readLine());
                }catch(IOException e){
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }
        public int nextInt(){
            return Integer.parseInt(next());
        }
        public int[] readArray(int n){
            int []a=new int[n];
            for(int i=0;i<n;i++){
                a[i]=nextInt();
            }
            return a;
        }
        public long nextLong(){
            return Long.parseLong(next());
        }
    }
}