1455_B. 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.
```python
t = int(input())

for i in range(t):
   n = int(input())
   i=1
   sum=0
   cnt=0
   while sum<n:
       sum+=i
       cnt+=1
       i+=1
   if sum==n or sum-n>1:
       print(cnt)
   else:
       print(cnt+1)


```