write a go solution for Description:
You are given a sequence of n integers a_1,a_2,ldots,a_n.

You have to construct two sequences of integers b and c with length n that satisfy:

- for every i (1<=i<=n) b_i+c_i=a_i
- b is non-decreasing, which means that for every 1<i<=n, b_i>=b_i-1 must hold
- c is non-increasing, which means that for every 1<i<=qn, c_i<=c_i-1 must hold

You have to minimize max(b_i,c_i). In other words, you have to minimize the maximum number in sequences b and c.

Also there will be q changes, the i-th change is described by three integers l,r,x. You should add x to a_l,a_l+1,ldots,a_r.

You have to find the minimum possible value of max(b_i,c_i) for the initial sequence and for sequence after each change.

Input Format:
The first line contains an integer n (1<=n<=10^5).

The secound line contains n integers a_1,a_2,ldots,a_n (1<=i<=n, -10^9<=a_i<=10^9).

The third line contains an integer q (1<=q<=10^5).

Each of the next q lines contains three integers l,r,x (1<=l<=r<=n,-10^9<=x<=10^9), desribing the next change.

Output Format:
Print q+1 lines.

On the i-th (1<=i<=q+1) line, print the answer to the problem for the sequence after i-1 changes.

Note:
In the first test:

- The initial sequence a=(2,-1,7,3). Two sequences b=(-3,-3,5,5),c=(5,2,2,-2) is a possible choice.
- After the first change a=(2,-4,4,0). Two sequences b=(-3,-3,5,5),c=(5,-1,-1,-5) is a possible choice.
- After the second change a=(2,-4,6,2). Two sequences b=(-4,-4,6,6),c=(6,0,0,-4) is a possible choice.. Output only the code with no comments, explanation, or additional text.