Jumps

You are standing on the OX-axis at point 0 and you want to move to an integer point x > 0.

You can make several jumps. Suppose you're currently at point y (y may be negative) and jump for the k-th time. You can:

• either jump to the point y + k
• or jump to the point y - 1.

What is the minimum number of jumps you need to reach the point x?

Input

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

The first and only line of each test case contains the single integer x (1 ≤ x ≤ 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.

Example

Input

5 1 2 3 4 5

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.

inputFormat

Input

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

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

outputFormat

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.

Example

Input

5 1 2 3 4 5

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.

样例

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