CF 174（div2） C

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本文介绍了一个涉及序列操作的问题，包括添加、删除元素及求平均值等操作，并提供了一种高效解决方案，利用数组记录操作以便快速更新序列状态。

Bessie and the cows are playing with sequences and need your help. They start with a sequence, initially containing just the number 0, and perform n operations. Each operation is one of the following:

Add the integer x_i to the first a_i elements of the sequence.
Append an integer k_i to the end of the sequence. (And hence the size of the sequence increases by 1)
Remove the last element of the sequence. So, the size of the sequence decreases by one. Note, that this operation can only be done if there are at least two elements in the sequence.

After each operation, the cows would like to know the average of all the numbers in the sequence. Help them!

Input

The first line contains a single integer n (1 ≤ n ≤ 2·10⁵) — the number of operations. The next n lines describe the operations. Each line will start with an integer t_i (1 ≤ t_i ≤ 3), denoting the type of the operation (see above). If t_i = 1, it will be followed by two integers a_i, x_i (|x_i| ≤ 10³; 1 ≤ a_i). If t_i = 2, it will be followed by a single integer k_i (|k_i| ≤ 10³). If t_i = 3, it will not be followed by anything.

It is guaranteed that all operations are correct (don't touch nonexistent elements) and that there will always be at least one element in the sequence.

Output

Output n lines each containing the average of the numbers in the sequence after the corresponding operation.

The answer will be considered correct if its absolute or relative error doesn't exceed 10^- 6.

Sample test(s)

Input

Output

Input

Output

Note

In the second sample, the sequence becomes $\text{[math]}$

yy题，感觉用线段树也可以，不过这题不用这么麻烦，因为每次修改的区间的起点是定值，所以yy一种直接的数据组织方式，类似扫描线。我的方法是开两个数组，add记录从起点到第i个点范围内加了多少，a记录加入到尾部的那些数。用num记录目前有多少个数，total记录所有数的和。唯一要注意的是3操作，把末尾add“挪”向前一个，然后别忘了把它清零。

#include <cstdio>
#include <cstring>
#include <iostream>
#include <algorithm>
#include <vector>
#define LL long long
using namespace std;
const int maxn = 200000  + 5;

LL add[maxn],a[maxn];

int main(){
    int n;
    while(cin >> n){
        LL total = 0;
        int num = 1;
        a[1] = 0;
        memset(add,0,sizeof(add));
        double ans;
        for(int i = 0;i < n;i++){
            LL op,x,y;
            cin >> op;
            if(op == 1){
                cin >> x >> y;
                total += x*y;
                add[x] += y;
            }
            else if(op == 2){
                cin >> x;
                total += x;
                num++;
                a[num] = x;
            }
            else{
                if(num == 1) continue;
                total = total - a[num] - add[num];
                add[num-1] += add[num];
                add[num] = 0;
                num--;
            }
            ans = (double)total/num;
            printf("%.6lf\n",ans);
        }
    }
    return 0;
}