For two sequences S and T of length N consisting of 0 and 1, let us define f(S, T) as follows:

* Consider repeating the following operation on S so that S will be equal to T. f(S, T) is the minimum possible total cost of those operations.

* Change S_i (from 0 to 1 or vice versa). The cost of this operation is D \times C_i, where D is the number of integers j such that S_j \neq T_j (1 \leq j \leq N) just before this change.



There are 2^N \times (2^N - 1) pairs (S, T) of different sequences of length N consisting of 0 and 1. Compute the sum of f(S, T) over all of those pairs, modulo (10^9+7).

Constraints

* 1 \leq N \leq 2 \times 10^5
* 1 \leq C_i \leq 10^9
* All values in input are integers.

Input

Input is given from Standard Input in the following format:


N
C_1 C_2 \cdots C_N


Output

Print the sum of f(S, T), modulo (10^9+7).

Examples

Input

1
1000000000


Output

999999993


Input

2
5 8


Output

124


Input

5
52 67 72 25 79


Output

269312
#include <iostream>
#include <algorithm>

using namespace std;
typedef long long ll;
ll mod = 1000000007;
ll pw(ll a, ll x){
	ll ret = 1;
	while(x){
		while(!(x&1)){
			(a *= a) %= mod;
			x /= 2;
		}
		(ret *= a) %= mod;
		x--;
	}
	return ret;
}

int c[200010];
ll sum[200010];
int main(){
	ll i,n;
	cin >> n;
	for(i=0;i<n;i++){
		cin >> c[i];
	}
	sort(c,c + n);
	ll ans = 0;
	for(i=0;i<n;i++){
		(ans += pw(2,2*n - 2)*(n + 1 - i)%mod*c[i]%mod) %= mod;
	}
	cout << ans << endl;
}