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1426C · Increase and Copy

1100 · binary search, constructive algorithms, math

Problem: Initially, you have the array aa consisting of one element 11 (a=[1]a = [1]).

In one move, you can do one of the following things:

  • Increase some (single) element of aa by 11 (choose some ii from 11 to the current length of aa and increase aia_i by one);
  • Append the copy of some (single) element of aa to the end of the array (choose some ii from 11 to the current length of aa and append aia_i to the end of the array).

For example, consider the sequence of five moves:

  1. You take the first element a1a_1, append its copy to the end of the array and get a=[1,1]a = [1, 1].
  2. You take the first element a1a_1, increase it by 11 and get a=[2,1]a = [2, 1].
  3. You take the second element a2a_2, append its copy to the end of the array and get a=[2,1,1]a = [2, 1, 1].
  4. You take the first element a1a_1, append its copy to the end of the array and get a=[2,1,1,2]a = [2, 1, 1, 2].
  5. You take the fourth element a4a_4, increase it by 11 and get a=[2,1,1,3]a = [2, 1, 1, 3].

Your task is to find the minimum number of moves required to obtain the array with the sum at least nn.

You have to answer tt independent test cases.

Input Format: The first line of the input contains one integer tt (1t10001 \le t \le 1000) — the number of test cases. Then tt test cases follow.

The only line of the test case contains one integer nn (1n1091 \le n \le 10^9) — the lower bound on the sum of the array.

Output Format: For each test case, print the answer: the minimum number of moves required to obtain the array with the sum at least nn.

Sample Cases

Case 1

Input

5
1
5
42
1337
1000000000

Output

0
3
11
72
63244

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