Score : $400$ points

Problem Statement

You are given a sequence of $N$ non-negative integers: $A_1,A_2,\cdots,A_N$.

Consider inserting a + or - between each pair of adjacent terms to make one formula.

There are $2^{N-1}$ such ways to make a formula. Such a formula is called good when the following condition is satisfied:

• - does not occur twice or more in a row.

Find the sum of the evaluations of all good formulae. We can prove that this sum is always a non-negative integer, so print it modulo $(10^9+7)$.

Constraints

• $1 \leq N \leq 10^5$
• $1 \leq A_i \leq 10^9$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$

$A_1$ $A_2$ $\cdots$ $A_N$

Output

Print the sum modulo $(10^9+7)$.

3
3 1 5

15

We have the following three good formulae:

• $3+1+5=9$
• $3+1-5=-1$
• $3-1+5=7$

Note that $3-1-5$ is not good since- occurs twice in a row in it. Thus, the answer is $9+(-1)+7=15$.

4
1 1 1 1

10

We have the following five good formulae:

• $1+1+1+1=4$
• $1+1+1-1=2$
• $1+1-1+1=2$
• $1-1+1+1=2$
• $1-1+1-1=0$

Thus, the answer is $4+2+2+2+0=10$.

10
866111664 178537096 844917655 218662351 383133839 231371336 353498483 865935868 472381277 579910117

279919144

Print the sum modulo $(10^9+7)$.