Tricoin
Problem 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:
1. He puts 1 coin in the 1st row.
2. then puts 2 coins in the 2nd row.
3. 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 <=109
Subtasks
Subtask 1 (48 points) : 1<=N<=105
Subtask 2 (52 points) : 1<=N<=109
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
Logic Test Case 1
Input (stdin)
3
3 5 7
Expected Output
2
2
3
Logic Test Case 2
Input (stdin)
7
7 5 4 3 8 9 5
Expected Output
3
2
2
2
3
3
2
code area
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