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 <bits/stdc++.h>
#define mod 1000000007
#define rep(i,n) for(int i=0;(i)<(n);i++)
typedef long long ll;
using namespace std;
ll h_pow(ll x,ll n){
    ll ans = 1ll;
    while(n>0){
        if(n&1){
            ans = (ans*x)%mod;
        }
        n >>= 1;
        x = (x*x)%mod;
    }
    return ans;
}
int main (){
    int n; cin >> n;
    vector<int> c(n);
    rep(i,n) cin >> c[i];
    sort(c.begin(),c.end());
    ll coef = h_pow(2,n-1);
    ll diff = h_pow(2,n-2);
    ll ans = 0;
    for(int i=n-1;i>=0;i--){
        ans = (ans + coef*c[i])%mod;
        coef = (coef+diff)%mod;
    }
    cout << (ans*h_pow(2,n))%mod << endl;
}


