https://www.codechef.com/practice/course/binary-search/INTBINS01/problems/TRICOIN
Difficulty: 1075
Topics: Binary Search
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?
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.
For each test case, output a single line containing an integer corresponding to the maximum possible height of the triangle that Chef can get.
- 1 ≤ T ≤ 100
- 1 ≤ N ≤ 109
- Subtask 1 (48 points) : 1 ≤ N ≤ 105
- Subtask 2 (52 points) : 1 ≤ N ≤ 109
Sample 1: 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.