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>
#define fastio()                  \
    ios_base::sync_with_stdio(0); \
    cin.tie(0);                   \
    cout.tie(0)
#define pb push_back
#define show(x) cout << (#x) << " : " << x << endl;
#define ll long long
#define ull unsigned long long
#define ld long double
#define pow power
#define mp make_pair
#define ff first
#define ss second
#define pii pair<ll, ll>
#define sq(x) ((x) * (x))
#define all(v) v.begin(), v.end()
#define rall(v) v.rbegin(), v.rend()
#define siz(a) int((a).size())
#define For(i,a,b) for(int (i)=(a);(i) < (b); ++(i))
#define endl "\n"
#define pi 3.14159265
const ll mod = 1000 * 1000 * 1000 + 7;
const ll mod1 = 998244353;
const ll INF     = 1ll*1000*1000*1000*1000*1000*1000 + 7; 
using namespace std;

ll power(ll x, ll y) 
{ 
   ll res = 1;      
  
   
    while (y > 0) 
    { 
       
        if (y & 1) 
            res = (long long)(res*x); 
  

        y = y>>1; 

        x = (long long)(x*x);

        //cout<<x<<'\n'; 
    } 
    return res; 
} 



// Stolen Templates
template <typename T>
T MIN(T first) { return first; }

template <typename T, typename... Args>
T MIN(T first, Args... args) { return min(first, MIN(args...)); }


template <typename T>
T MAX(T first) { return first; }

template <typename T, typename... Args>

T MAX(T first, Args... args) { return max(first, MAX(args...)); }
// Stolen Templates end here




int main()
{

#ifndef ONLINE_JUDGE    
freopen("input.txt","r",stdin);
freopen("output.txt","w",stdout);
#endif

fastio();

    ll T;
    cin>>T;

    while(T--)
    {
        ll n;
        cin>>n;
        ll ans=0;
        for(ll a=1;a*a<=2*n;a++) {
            ll val =a*a;
            val-=1;
            if (val%2==0 and (val/2)>=a)
                ans+=1;
        }
        cout<<ans<<endl;

    }

return 0;
}

// check all product based operations for integer overflow
// careful of renamed variables especially in loops