Jumps

Description:

Input:

The first line contains a single integer $$$t$$$ ($$$1 \le t \le 1000$$$) — the number of test cases.

The first and only line of each test case contains the single integer $$$x$$$ ($$$1 \le x \le 10^6$$$) — the destination point.

Output:

For each test case, print the single integer — the minimum number of jumps to reach $$$x$$$. It can be proved that we can reach any integer point $$$x$$$.

Sample Input:

5
1
2
3
4
5

Sample Output:

1
3
2
3
4

Note:

In the first test case $$$x = 1$$$, so you need only one jump: the $$$1$$$-st jump from $$$0$$$ to $$$0 + 1 = 1$$$.

In the second test case $$$x = 2$$$. You need at least three jumps:

• the $$$1$$$-st jump from $$$0$$$ to $$$0 + 1 = 1$$$;
• the $$$2$$$-nd jump from $$$1$$$ to $$$1 + 2 = 3$$$;
• the $$$3$$$-rd jump from $$$3$$$ to $$$3 - 1 = 2$$$;

Two jumps are not enough because these are the only possible variants:

• the $$$1$$$-st jump as $$$-1$$$ and the $$$2$$$-nd one as $$$-1$$$ — you'll reach $$$0 -1 -1 =-2$$$;
• the $$$1$$$-st jump as $$$-1$$$ and the $$$2$$$-nd one as $$$+2$$$ — you'll reach $$$0 -1 +2 = 1$$$;
• the $$$1$$$-st jump as $$$+1$$$ and the $$$2$$$-nd one as $$$-1$$$ — you'll reach $$$0 +1 -1 = 0$$$;
• the $$$1$$$-st jump as $$$+1$$$ and the $$$2$$$-nd one as $$$+2$$$ — you'll reach $$$0 +1 +2 = 3$$$;

In the third test case, you need two jumps: the $$$1$$$-st one as $$$+1$$$ and the $$$2$$$-nd one as $$$+2$$$, so $$$0 + 1 + 2 = 3$$$.

In the fourth test case, you need three jumps: the $$$1$$$-st one as $$$-1$$$, the $$$2$$$-nd one as $$$+2$$$ and the $$$3$$$-rd one as $$$+3$$$, so $$$0 - 1 + 2 + 3 = 4$$$.