Find The Array

Let's call an array a consisting of n positive (greater than 0) integers beautiful if the following condition is held for every i from 1 to n: either a_i = 1, or at least one of the numbers a_i - 1 and a_i - 2 exists in the array as well.

For example:

• the array [5, 3, 1] is beautiful: for a_1, the number a_1 - 2 = 3 exists in the array; for a_2, the number a_2 - 2 = 1 exists in the array; for a_3, the condition a_3 = 1 holds;
• the array [1, 2, 2, 2, 2] is beautiful: for a_1, the condition a_1 = 1 holds; for every other number a_i, the number a_i - 1 = 1 exists in the array;
• the array [1, 4] is not beautiful: for a_2, neither a_2 - 2 = 2 nor a_2 - 1 = 3 exists in the array, and a_2 ≠ 1;
• the array [2] is not beautiful: for a_1, neither a_1 - 1 = 1 nor a_1 - 2 = 0 exists in the array, and a_1 ≠ 1;
• the array [2, 1, 3] is beautiful: for a_1, the number a_1 - 1 = 1 exists in the array; for a_2, the condition a_2 = 1 holds; for a_3, the number a_3 - 2 = 1 exists in the array.

You are given a positive integer s. Find the minimum possible size of a beautiful array with the sum of elements equal to s.

Input

The first line contains one integer t (1 ≤ t ≤ 5000) — the number of test cases.

Then t lines follow, the i-th line contains one integer s (1 ≤ s ≤ 5000) for the i-th test case.

Output

Print t integers, the i-th integer should be the answer for the i-th testcase: the minimum possible size of a beautiful array with the sum of elements equal to s.

Example

Input

4 1 8 7 42

Output

1 3 3 7

Note

Consider the example test:

1. in the first test case, the array [1] meets all conditions;
2. in the second test case, the array [3, 4, 1] meets all conditions;
3. in the third test case, the array [1, 2, 4] meets all conditions;
4. in the fourth test case, the array [1, 4, 6, 8, 10, 2, 11] meets all conditions.

inputFormat

Input

The first line contains one integer t (1 ≤ t ≤ 5000) — the number of test cases.

Then t lines follow, the i-th line contains one integer s (1 ≤ s ≤ 5000) for the i-th test case.

outputFormat

Output

Print t integers, the i-th integer should be the answer for the i-th testcase: the minimum possible size of a beautiful array with the sum of elements equal to s.

Example

Input

4 1 8 7 42

Output

1 3 3 7

Note

Consider the example test:

1. in the first test case, the array [1] meets all conditions;
2. in the second test case, the array [3, 4, 1] meets all conditions;
3. in the third test case, the array [1, 2, 4] meets all conditions;
4. in the fourth test case, the array [1, 4, 6, 8, 10, 2, 11] meets all conditions.

样例

4
1
8
7
42

1
3
3
7

</p>