## 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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