Sum of Digits
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You are given an array of N distinct numbers. Now, we call the Digit Value of a number to be the sum of its digits..

Now, a subset is a set of not-necessarily-contiguous array elements. We call the value of a set to be the the maximum over the Digit Value of all elements it contains.

Now, you need to find the summation of the values of all $2^{N}-1$ non-empty subsets of this array. As the answer can be rather large, print it Modulo $10^9+7$. Can you do it ?

Input Format :

The first line contains a single integer N. The next line contains N space separated integers, where the $i^{th}$ integer denotes $A[i]$.

Output Format :

Print the summation of the value of each non-empty subset of the given array Modulo $10^9+7$.

Constraints :

$1 \le N \le 10^{5}$

$0 \le A[i] \le 10^{18}$

SAMPLE INPUT
3
10 20 30
SAMPLE OUTPUT
17
Explanation

The subsets of this array and their values are :

1. (10) : 1

2. (20) : 2

3. (30) : 3

4. (10,20) : 2

5. (10, 30) : 3

6. (20,30) : 3

7. (10,20,30 ) : 3

Thus, the final answer is $(1+2+3+2+3+3+3 )$ = $17$

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: 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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## This Problem was Asked in

Challenge Name

Accolite Java Developer Hiring Challenge

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• Algorithms > String Algorithms