Codeforces Round 674 (Div. 3) |
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Finished |

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binary search

constructive algorithms

math

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C. Increase and Copy

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputInitially, you have the array $$$a$$$ consisting of one element $$$1$$$ ($$$a = [1]$$$).

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

- Increase some (single) element of $$$a$$$ by $$$1$$$ (choose some $$$i$$$ from $$$1$$$ to the current length of $$$a$$$ and increase $$$a_i$$$ by one);
- Append the copy of some (single) element of $$$a$$$ to the end of the array (choose some $$$i$$$ from $$$1$$$ to the current length of $$$a$$$ and append $$$a_i$$$ to the end of the array).

For example, consider the sequence of five moves:

- You take the first element $$$a_1$$$, append its copy to the end of the array and get $$$a = [1, 1]$$$.
- You take the first element $$$a_1$$$, increase it by $$$1$$$ and get $$$a = [2, 1]$$$.
- You take the second element $$$a_2$$$, append its copy to the end of the array and get $$$a = [2, 1, 1]$$$.
- You take the first element $$$a_1$$$, append its copy to the end of the array and get $$$a = [2, 1, 1, 2]$$$.
- You take the fourth element $$$a_4$$$, increase it by $$$1$$$ and get $$$a = [2, 1, 1, 3]$$$.

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

You have to answer $$$t$$$ independent test cases.

Input

The first line of the input contains one integer $$$t$$$ ($$$1 \le t \le 1000$$$) — the number of test cases. Then $$$t$$$ test cases follow.

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

Output

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

Example

Input

5 1 5 42 1337 1000000000

Output

0 3 11 72 63244

Codeforces (c) Copyright 2010-2024 Mike Mirzayanov

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