B - Sum of Three Terms /

### 問題文

• 任意の i (1\leq i\leq N+2) に対して 0\leq A_i が成り立つ。
• 任意の i (1\leq i\leq N) に対して、S_i = A_{i} + A_{i+1} + A_{i+2} が成り立つ。

### 制約

• 1\leq N\leq 3\times 10^5
• 0\leq S_i\leq 10^9

### 入力

N
S_1 \ldots S_N


### 出力

A_1 \ldots A_{N+2}


### 入力例 1

5
6 9 6 6 5


### 出力例 1

Yes
0 4 2 3 1 2 2


• 6 = 0 + 4 + 2
• 9 = 4 + 2 + 3
• 6 = 2 + 3 + 1
• 6 = 3 + 1 + 2
• 5 = 1 + 2 + 2

### 入力例 2

5
0 1 2 1 0


### 出力例 2

No


### 入力例 3

1
10


### 出力例 3

Yes
0 0 10


Score : 500 points

### Problem Statement

You are given a sequence of N integers S = (S_1, \ldots, S_N). Determine whether there is a sequence of N+2 integers A = (A_1, \ldots, A_{N+2}) that satisfies the conditions below.

• 0\leq A_i for every i (1\leq i\leq N+2).
• S_i = A_{i} + A_{i+1} + A_{i+2} for every i (1\leq i\leq N).

If it exists, print one such sequence.

### Constraints

• 1\leq N\leq 3\times 10^5
• 0\leq S_i\leq 10^9

### Input

Input is given from Standard Input from the following format:

N
S_1 \ldots S_N


### Output

If there is a sequence A that satisfies the conditions, print Yes; otherwise, print No. In the case of Yes, print an additional line containing the elements of such a sequence A, separated by spaces.

A_1 \ldots A_{N+2}


If there are multiple sequences satisfying the conditions, you may print any of them.

### Sample Input 1

5
6 9 6 6 5


### Sample Output 1

Yes
0 4 2 3 1 2 2


We can verify that S_i = A_i + A_{i+1} + A_{i+2} for every i (1\leq i\leq N), as follows.

• 6 = 0 + 4 + 2.
• 9 = 4 + 2 + 3.
• 6 = 2 + 3 + 1.
• 6 = 3 + 1 + 2.
• 5 = 1 + 2 + 2.

### Sample Input 2

5
0 1 2 1 0


### Sample Output 2

No


### Sample Input 3

1
10


### Sample Output 3

Yes
0 0 10