Coins And Triangle TRICOIN

All submissions for this problem are available.<h3> Read problems statements in Mandarin Chinese , Russian and Vietnamese as well.</h3>

Chef belongs to a very rich family which owns many gold mines. Today, he brought N gold coins and decided to form a triangle using these coins. Isn't it strange?

Chef has a unusual way of forming a triangle using gold coins, which is described as follows:

• He puts 1 coin in the 1^st row.
• then puts 2 coins in the 2^nd row.
• then puts 3 coins in the 3^rd row.
• and so on as shown in the given figure.

Chef is interested in forming a triangle with maximum possible height using at most N coins. Can you tell him the maximum possible height of the triangle?

Input

The first line of input contains a single integer T denoting the number of test cases.

The first and the only line of each test case contains an integer N denoting the number of gold coins Chef has.

Output

For each test case, output a single line containing an integer corresponding to the maximum possible height of the triangle that Chef can get.

Constraints

• 1 ≤ T ≤ 100
• 1 ≤ N ≤ 10⁹

Subtasks

• Subtask 1 (48 points) : 1 ≤ N ≤ 10⁵</li>
• Subtask 2 (52 points) : 1 ≤ N ≤ 10⁹</li> </ul>

  Example

  Input
  3
  3
  5
  7
  
  Output
  2
  2
  3
  

  Explanation

  • Test 1: Chef can't form a triangle with height > 2 as it requires atleast 6 gold coins.
  • Test 2: Chef can't form a triangle with height > 2 as it requires atleast 6 gold coins.
  • Test 3: Chef can't form a triangle with height > 3 as it requires atleast 10 gold coins.