7360: CodeChef TRICOIN - Coins And Triangle
[Creator : ]
Description
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 1st row.
- then puts 2 coins in the 2nd row.
- then puts 3 coins in the 3rd 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
$1 ≤ T ≤ 100$
$1 ≤ N ≤ 10^9$
$1 ≤ N ≤ 10^9$
Sample 1 Input
3
3
5
7
Sample 1 Output
2
2
3
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.
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.