#include <algorithm>
#include <bitset>
#include <cmath>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <deque>
#include <functional>
#include <iostream>
#include <map>
#include <queue>
#include <set>
#include <stack>
#include <string>
#include <vector>
#define lowbit(x) (x & -x)
using namespace std;
typedef long long LL;
typedef pair<int, int> PII;
const int INF = 0x3f3f3f3f;
const double PI = acos(-1.0), eps = 1e-6;
const int N = 1e5 + 10;

int main(int argc, char const *argv[]) {
    int t, n, res;
    cin >> t;
    while (t--) {
        scanf("%d", &n);
        int l = 1, r = 5e8;
        res = 0;
        while (l <= r) {
            int mid = l + r >> 1;
            LL x = mid * 2 + 1;
            x = (x * x + 1) >> 1;
            if (x <= n) {
                res = mid;
                l = mid + 1;
            } else {
                r = mid - 1;
            }
        }
        printf("%d\n", res);
    }
    return 0;
}

### Prompt

In cpp, your task is to solve the following 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.

### Response

```cpp
#include <algorithm>
#include <bitset>
#include <cmath>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <deque>
#include <functional>
#include <iostream>
#include <map>
#include <queue>
#include <set>
#include <stack>
#include <string>
#include <vector>
#define lowbit(x) (x & -x)
using namespace std;
typedef long long LL;
typedef pair<int, int> PII;
const int INF = 0x3f3f3f3f;
const double PI = acos(-1.0), eps = 1e-6;
const int N = 1e5 + 10;

int main(int argc, char const *argv[]) {
    int t, n, res;
    cin >> t;
    while (t--) {
        scanf("%d", &n);
        int l = 1, r = 5e8;
        res = 0;
        while (l <= r) {
            int mid = l + r >> 1;
            LL x = mid * 2 + 1;
            x = (x * x + 1) >> 1;
            if (x <= n) {
                res = mid;
                l = mid + 1;
            } else {
                r = mid - 1;
            }
        }
        printf("%d\n", res);
    }
    return 0;
}

```