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;
#define ll                long long
#define pb                push_back
#define vi                vector<int>
#define vl                vector<long long>
#define vll               vector<pair<long long,long long>>
#define vii               vector<pair<int,int>>
#define vvi               vector<vector<int>>
#define maxq(x)           priority_queue<x>
#define minq(x)           priority_queue<x,vector<x>,greater<x>>
#define graph             map<int,vi>
#define vvl               vector<vector<long long>>
#define pb                push_back
#define ppb               pop_back
#define pf                push_front
#define ppf               pop_front
#define all(x)            (x).begin(),(x).end()
#define uniq(v)           (v).erase(unique(all(v)),(v).end())
#define sz(x)             (int)((x).size())
#define f                 first
#define s                 second
#define pii               pair<int,int>
#define rep(i,a,b)        for(int i=a;i<b;i++)
#define rrep(i,a,b)       for(int i = a;i>=b;i--)
#define mem1(a)           memset(a,-1,sizeof(a))
#define mem0(a)           memset(a,0,sizeof(a))
#define ppc               __builtin_popcount
#define ppcll             __builtin_popcountll
# define quick ios_base::sync_with_stdio(false);cin.tie(0);cout.tie(0);
int main() 
{  
  quick
  int t = 1;
  cin>>t;
  while(t--)
  {
     int n;
     cin>>n;
     int cnt = 0;
     int s = 1,e = 100000;
     while(s<=e)
     {
         ll mid = (s + e)/2;
         ll odd = 2*mid + 1;
         ll b = (odd*odd - 1)/2;
         ll c = odd*odd - b;
         if(c>n || odd>n || b>n)
         e = mid - 1;
         else
         {
             s = mid + 1;
             cnt = mid;
         }
         
     }
     cout<<cnt<<endl;
  }
  return 0;
   
}