13:I[87,["736","static/chunks/89fc4f0e-9e200ae6a0166583.js","401","static/chunks/363642f4-32903b9154b7835a.js","153","static/chunks/153-58eddeb032cc4608.js","131","static/chunks/131-05ce00cfd760e12b.js","87","static/chunks/87-b76b60eef573119a.js","286","static/chunks/app/problem/%5Bid%5D/page-45cf3875257fc32e.js"],"Header"] 14:I[1742,["736","static/chunks/89fc4f0e-9e200ae6a0166583.js","401","static/chunks/363642f4-32903b9154b7835a.js","153","static/chunks/153-58eddeb032cc4608.js","131","static/chunks/131-05ce00cfd760e12b.js","87","static/chunks/87-b76b60eef573119a.js","286","static/chunks/app/problem/%5Bid%5D/page-45cf3875257fc32e.js"],"ProblemView"] 15:T71f,

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 $$$k$$$.

Input

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

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

Output

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

Note

In the first example:

From $$$1$$$ to $$$1$$$: the cost is $$$0$$$,
From $$$1$$$ to $$$2$$$: $$$1 \rig

Wonderful Jump

Examples