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.*;
public class Solution {
    static StringBuilder sb;
    static FastReader in;
    static long mod=1000000007;
    public static void main(String[] args) throws Exception {
        sb = new StringBuilder();
        in = new FastReader(System.in);
        int t = in.nextInt();
        while(t-->0)
            solve();
        System.out.print(sb);
    }
    static void solve()throws IOException {
        int i, j;
        int n=in.nextInt();
        int x=1, diff=4, cnt=0;
        while(x+diff<=n) {
            cnt++;
            x+=diff;
            diff+=4;
        }
        sb.append(cnt+"\n");
    }
    static void sorter(long a[]) {
        ArrayList<Long> ar=new ArrayList<>();
        for(int i=0;i<a.length;i++)
            ar.add(a[i]);
        Collections.sort(ar);
        for(int i=0;i<ar.size();i++)
            a[i]=ar.get(i);
    }
    static long power(long x, long y, long p) {  
        long res = 1;       
        x = x % p;  
        if (x == 0) return 0;   
        while (y > 0) {
            if((y & 1)==1) 
                res = (res * x) % p;  
            y = y >> 1;  
            x = (x * x) % p;  
        } 
        return res%p; 
    }
    static long mul(long x, long y, long m) {long ans = x*y;return (ans>=m ? ans%m : ans);}
}
class Pair { 
    int x; 
    int y; 
    public Pair(int x, int y) 
    {
        this.x = x; 
        this.y = y; 
    } 
}
class sortbyX implements Comparator<Pair> { 
    public int compare(Pair a, Pair b) 
    { 
        return a.x - b.x; 
    } 
}
class FastReader {
    byte[] buf = new byte[2048];
    int index, total;
    InputStream in;
    FastReader(InputStream is) {
        in = is;
    }
    int scan() throws IOException {
        if (index >= total) {
            index = 0;
            total = in.read(buf);
            if (total <= 0) {
                return -1;
            }
        }
        return buf[index++];
    }
    String next() throws IOException {
        int c;
        for (c = scan(); c <= 32; c = scan()) ;
        StringBuilder sb = new StringBuilder();
        for (; c > 32; c = scan()) {
            sb.append((char) c);
        }
        return sb.toString();
    }
    int nextInt() throws IOException {
        int c, val = 0;
        for (c = scan(); c <= 32; c = scan()) ;
        boolean neg = c == '-';
        if (c == '-' || c == '+') {
            c = scan();
        }
        for (; c >= '0' && c <= '9'; c = scan()) {
            val = (val << 3) + (val << 1) + (c & 15);
        }
        return neg ? -val : val;
    }
    long nextLong() throws IOException {
        int c;
        long val = 0;
        for (c = scan(); c <= 32; c = scan()) ;
        boolean neg = c == '-';
        if (c == '-' || c == '+') {
            c = scan();
        }
        for (; c >= '0' && c <= '9'; c = scan()) {
            val = (val << 3) + (val << 1) + (c & 15);
        }
        return neg ? -val : val;
    }
}