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:
/*
 * @Author: Mahbus 
 * @Date: 2021-02-15 21:20:30 
 * @Last Modified by: Mahbus
 * @Last Modified time: 2021-02-15 21:59:22
 */
#include <bits/stdc++.h>
#pragma GCC optimize("Ofast")
#pragma GCC target("avx,avx2,fma")
#pragma GCC optimization("unroll-loops")
using namespace std;
typedef long long ll;
#define _cin                      \
    ios_base::sync_with_stdio(0); \
    cin.tie(0);
#define endl "\n"
#define pb push_back
#define rp(i, b) for (ll i = 0; i < b; ++i)
#define rpd(i, a) for (ll i = a; i >= 0; --i)
#define mp make_pair
#define hell 1000000007
#define vvll vector<vector<ll>>
#define vll vector<ll>
#define mll map<ll, ll>
#define sz(x) (ll) x.size()
#define sll set<ll>
#define pll pair<ll, ll>
#define F first
#define S second
#define eb emplace_back
#define ppb pop_back
#define pf push_front
#define ppf pop_front
#define all(x) x.begin(), x.end()
#define clr(x) memset(x, 0, sizeof(x))
#define sortall(x) sort(all(x))
#define tr(it, a) for (auto it = a.begin(); it != a.end(); it++)
#define PI 3.1415926535897932384626
#define deb(x) cout << #x << "=" << x << endl
#define deb2(x, y) cout << #x << "=" << x << "," << #y << "=" << y << endl
#define precise(x) cout << fixed << setprecision(x)
const ll MAX = 1000004;
const ll INF = 1e18L + 5;
template <class T, class U>
void chmin(T &t, const U &u)
{
    if (t > u)
        t = u;
}
template <class T, class U>
void chmax(T &t, const U &u)
{
    if (t < u)
        t = u;
}
template <typename Head, typename... Tail>
void debug_out(Head H, Tail... T)
{
    cerr << " " << H;
    debug_out(T...);
}
template <typename Arg1>
void pn(Arg1 &&arg1)
{
    cout << arg1 << "\n";
}
template <typename Arg1, typename... Args>
void pn(Arg1 &&arg1, Args &&...args)
{
    cout << arg1 << "\n";
    pn(args...);
}
template <typename Arg1>
void ps(Arg1 &&arg1)
{
    cout << arg1 << " ";
}
template <typename Arg1, typename... Args>
void ps(Arg1 &&arg1, Args &&...args)
{
    cout << arg1 << " ";
    ps(args...);
}
template <typename Arg1>
void read(Arg1 &&arg1)
{
    cin >> arg1;
}
template <typename Arg1, typename... Args>
void read(Arg1 &&arg1, Args &&...args)
{
    cin >> arg1;
    read(args...);
}

void solve()
{
    ll n;
    read(n);
    ll k = sqrt(2 * n - 1);
    ll odd = k / 2;
    if (k & 1)
        odd++;
    pn(odd - 1);
}

int main()
{

    _cin
        ll tc;
    cin >> tc;
    while (tc--)
    {
        solve();
    }
}