Triple Operations
Description
On the board Ivy wrote down all integers from $l$ to $r$, inclusive.
In an operation, she does the following:
- pick two numbers $x$ and $y$ on the board, erase them, and in their place write the numbers $3x$ and $\lfloor \frac{y}{3} \rfloor$. (Here $\lfloor \bullet \rfloor$ denotes rounding down to the nearest integer).
What is the minimum number of operations Ivy needs to make all numbers on the board equal $0$? We have a proof that this is always possible.
The first line contains an integer $t$ ($1 \leq t \leq 10^4$) — the number of test cases.
The only line of each test case contains two integers $l$ and $r$ ($1 \leq l < r \leq 2 \cdot 10^5$).
For each test case, output a single integer — the minimum number of operations needed to make all numbers on the board equal $0$.
Input
The first line contains an integer $t$ ($1 \leq t \leq 10^4$) — the number of test cases.
The only line of each test case contains two integers $l$ and $r$ ($1 \leq l < r \leq 2 \cdot 10^5$).
Output
For each test case, output a single integer — the minimum number of operations needed to make all numbers on the board equal $0$.
4
1 3
2 4
199999 200000
19 84
5
6
36
263
Note
In the first test case, we can perform $5$ operations as follows: $$ 1,2,3 \xrightarrow[x=1,\,y=2]{} 3,0,3 \xrightarrow[x=0,\,y=3]{} 1,0,3 \xrightarrow[x=0,\,y=3]{} 1,0,1 \xrightarrow[x=0,\,y=1]{} 0,0,1 \xrightarrow[x=0,\,y=1]{} 0,0,0 .$$