Mancunian And Naughty Numbers
Tag(s):

## Easy, Number Theory

Problem
Editorial
Analytics

Mancunian, our favourite football fan, is a die-hard supporter of Manchester United Football Club. Being so, he is desperate to attend the grand unveiling of Jose Mourinho as the next manager of the club. But, his arch-nemesis Liverbird (who is a Liverpool fan) wants him to fail. Knowing that Mancunian is weak at mathematics, he has given him a problem to solve before the ceremony. Can you help Mancunian do it and thwart the evil plans of Liverbird?

A $naughty \ number$ is one whose number of distinct prime factors is equal to the number of digits in its decimal representation. The number $1$ is considered a naughty number.

Given $Q$ queries, each query specifying two integers $a$ and $b$, find the number of $naughty \ numbers$ lying between $a$ and $b$ (both included).

### Input format

The first line contains an integer $Q$ denoting the number of queries.
Each of the next $Q$ lines consists of two integers $a$ and $b$ denoting the range for this query.

### Output format

Print $Q$ lines. The $ith$ line contains the answer for the $ith$ query.

### Constraints

• $1 \le Q \le 50,000$
• $1 \le a \le b \le 100,000$
SAMPLE INPUT
3
1 10
55 59
100 105

SAMPLE OUTPUT
9
4
2

Explanation

In the range $1$-$10$, all numbers except $6$ are naughty numbers.
In the range $55$-$59$, the naughty numbers are $55$, $56$, $57$ and $58$.
In the range $100$-$105$, only $102$ and $105$ are naughty numbers.

Time Limit: 2.0 sec(s) for each input file.
Memory Limit: 256 MB
Source Limit: 1024 KB
Marking Scheme: Marks are awarded when all the testcases pass.
Allowed Languages: C, C++, C++14, Clojure, C#, D, Erlang, F#, Go, Groovy, Haskell, Java, Java 8, JavaScript(Rhino), JavaScript(Node.js), Julia, Kotlin, Lisp, Lisp (SBCL), Lua, Objective-C, OCaml, Octave, Pascal, Perl, PHP, Python, Python 3, R(RScript), Racket, Ruby, Rust, Scala, Swift, Visual Basic

## CODE EDITOR

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## This Problem was Asked in

Challenge Name

August Easy '16

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