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Alexey works as a mathematician in a well-known company "WordCount". Since his project has been recently closed, he was given a rather strange kind of assignment as a replacement: he must write down consecutive integers in a certain range every month, and at the end of the month the accounting department makes some calculations that determine Alexey's salary.
Alexey's salary is calculated as follows: first, the accounting department finds such $x$ that there exists an integers with $x$ identical consecutive digits that among the integers that Alexey has written down, but there is no integer with $x+1$ identical consecutive digits. Then the integers that have $x$ identical consecutive digits are counted and the resulting amount is the Alexey's salary.
Alexey is a smart mathematician so he doesn't want to work for peanuts. Today he was given a work plan for the next $t$ months. During the $i$-th month he must write down integers from $l_i$ to $r_i$ inclusive. Help Alexey to calculate, what his salary would be each month, if the accounting department always does its calculations right.
The first line of input contains a single integer $t$, the number of months for which Alexey's salary should be calculated ($1 \le t \le 10^4$).
The $i$-th of the following $t$ lines contains two space-separated integers $l_i$ and $r_i$, the first and the last integer Alexey will write down during the $i$-th month ($1 \le l_i \le r_i \le 10^{18}$).
For each given month you should print a line with the calculated value of $x$ and Alexey's salary for that month.
1 312 348
3 1
1 223 329
2 17
Alexey writes down integers from $312$ and $348$ in the first example. There is an integer $333$ that has three identical consecutive digits. There are no other integers between those that have three identical consecutive digits, so the answer is "3 1
".
In the second example, there are no integers with three identical consecutive digits between $223$ and $329$. The integers with two identical consecutive digits can be divided into three groups:
There are exactly $17$ integers so the answer is "2 17
".