1455_B. Jumps_34888
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.
from collections import Counter, defaultdict, deque
import bisect
from sys import stdin, stdout
from itertools import repeat
import math


def inp(force_list=False):
    re = map(int, raw_input().split())
    if len(re) == 1 and not force_list:
        return re[0]
    return re

def inst():
    return raw_input().strip()

def gcd(x, y):
   while(y):
       x, y = y, x % y
   return x

mod = 1000000007

def my_main():
    kase = inp()
    ans = []
    j = 1
    l = [0]
    for i in range(1, 10000):
        l.append(l[-1]+i)
    # print l[:10]
    for i in range(kase):
        x = inp()
        idx = bisect.bisect_left(l, x)
        if l[idx]-x==1:
            print idx+1
        else:
            print idx
my_main()
