CF1768F.Wonderful Jump

普及/提高-

通过率：0%

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题目描述

You are given an array of positive integers $a_1,a_2,\ldots,a_n$ of length $n$ .

In one operation you can jump from index $i$ to index $j$ ( $1 \le i \le j \le n$ ) by paying $\min(a_i, a_{i + 1}, \ldots, a_j) \cdot (j - i)^2$ eris.

For all $k$ from $1$ to $n$ , find the minimum number of eris needed to get from index $1$ to index $k$ .

输入格式

The first line contains a single integer $n$ ( $2 \le n \le 4 \cdot 10^5$ ).

The second line contains $n$ integers $a_1,a_2,\ldots a_n$ ( $1 \le a_i \le n$ ).

输出格式

Output $n$ integers — the $k$ -th integer is the minimum number of eris needed to reach index $k$ if you start from index $1$ .

输入输出样例

输入#1
```
3
2 1 3
```
输出#1
```
0 1 2
```
输入#2
```
6
1 4 1 6 3 2
```
输出#2
```
0 1 2 3 6 8
```
输入#3
```
2
1 2
```
输出#3
```
0 1
```
输入#4
```
4
1 4 4 4
```
输出#4
```
0 1 4 8
```

说明/提示

In the first example:

From $1$ to $1$ : the cost is $0$ ,
From $1$ to $2$ : $1 \rightarrow 2$ — the cost is $\min(2, 1) \cdot (2 - 1) ^ 2=1$ ,
From $1$ to $3$ : $1 \rightarrow 2 \rightarrow 3$ — the cost is $\min(2, 1) \cdot (2 - 1) ^ 2 + \min(1, 3) \cdot (3 - 2) ^ 2 = 1 + 1 = 2$ .

In the fourth example from $1$ to $4$ : $1 \rightarrow 3 \rightarrow 4$ — the cost is $\min(1, 4, 4) \cdot (3 - 1) ^ 2 + \min(4, 4) \cdot (4 - 3) ^ 2 = 4 + 4 = 8$ .

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