A triangle number is a positive integer of the form $1+2+\dots+k$ . The first triangle numbers are $1$ , $3$ , $6$ , $10$ and $15$ .
Every positive integer can be represented as a sum of triangle numbers. For example, $42=21+21$ and $1337=1326+10+1$ .
Given a positive integer $n$ , determine the smallest number of triangle numbers that sum to $n$ .
The first line has an integer $t$ : the number of tests.
After that, each line has a positive integer $n$ .
For each test, print the smallest number of triangle numbers.