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 CPP):

Solution:
#include<bits/stdc++.h>
using namespace std;
typedef long long int ll;
typedef vector<ll> vl;
typedef pair<int,int> pi;
typedef pair<ll,ll> pl;
typedef vector<int> vi;
typedef pair<int, pair<int,int> > ppi;
const ll mod = 1e9+7;
const int MAXN=1e5+3;
void pvec(vl v){
    for(auto x:v){
        cout << x << " ";
    }cout << endl;
}
ll gcd(ll x, ll y){
    if(y==0){
        return x;
    }else{
        return gcd(y, x%y);
    }
}
 
ll binpow(ll a, ll b) {
    if(b==0){
        return 1;
    }
    ll res = 1;
    ll tmp = binpow(a,b/2);
    res = (tmp*tmp);
    if(b%2==1){
        res = (res*a);
    }
    return res;
}

void solve(){
    ll n;
    cin>>n;
    int v=0;
    for(ll a=3; (a*a-1)/2 < n; a+= 2){
        v++;
    }
    cout << v;
    cout << "\n";
}

int main(){
    ios_base::sync_with_stdio(false);
    cin.tie(0);cout.tie(0);
    int t=1;
    cin>>t;
    for(int i=1; i<=t; i++){
        solve();
    }
}