All Tracks Math Number Theory Primality Tests Problem

Shootout in London
Tag(s):

Easy, Math, Sieve

Problem
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There is a major shootout going on in London. Gunmen can be encountered in most of the streets and only a few of them are safe. Sherlock is given the responsibility to ensure the safety of the people by asking them to shift to the nearest safe street.
There are N streets on the road. The \(i^{th}\) street is denoted by the number \(A[i]\). Gunmen do not enter streets that are denoted by a prime number i.e. \(i^{th}\) street is safe, if \(A[i]\) is a prime.

Help Sherlock find the nearest safe street for people trapped in all the N streets i.e. print N integers, where the \(i^{th}\) integer is the index (1-based) of the nearest safe street. The distance between cities i and j is given by \(|i-j|\). For any city j, if there exists no safe city i, such that people of city j can move to city i, print 1 for it.

Note :

-If there are multiple nearest safe streets, print the one with the lower index.

Input:

The first line contains a single integer N denoting the number of cities. The next line contains N integers, where the \(i^{th}\) integer denotes \(A[i]\) .

Output:
Print the answer on a single line.

Constraints:

\( 1 \le N \le 5 \times 10^5 \)

\( 1 \le A[i] \le 10^6 \)

SAMPLE INPUT
5
1 2 3 1 6
SAMPLE OUTPUT
2 2 3 3 3
Explanation

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Time Limit: 1.0 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: Bash, 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, Swift-4.1, Visual Basic

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