SOLVE
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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 :
\( 1 \le N \le 10^{5} \)
\( 0 \le A[i] \le 10^{18} \)
The subsets of this array and their values are :
(10) : 1
(20) : 2
(30) : 3
(10,20) : 2
(10, 30) : 3
(20,30) : 3
(10,20,30 ) : 3
Thus, the final answer is \( (1+2+3+2+3+3+3 ) \) = \(17\)