Water Balance

题意翻译

给一个序列，每次可以将一个区间内的所有数都变成操作前这个区间的平均数，求最后能得到的字典序最小的结果。

题目描述

There are $ n $ water tanks in a row, $ i $ -th of them contains $ a_i $ liters of water. The tanks are numbered from $ 1 $ to $ n $ from left to right. You can perform the following operation: choose some subsegment $ [l, r] $ ( $ 1\le l \le r \le n $ ), and redistribute water in tanks $ l, l+1, \dots, r $ evenly. In other words, replace each of $ a_l, a_{l+1}, \dots, a_r $ by $ \frac{a_l + a_{l+1} + \dots + a_r}{r-l+1} $ . For example, if for volumes $ [1, 3, 6, 7] $ you choose $ l = 2, r = 3 $ , new volumes of water will be $ [1, 4.5, 4.5, 7] $ . You can perform this operation any number of times. What is the lexicographically smallest sequence of volumes of water that you can achieve? As a reminder: A sequence $ a $ is lexicographically smaller than a sequence $ b $ of the same length if and only if the following holds: in the first (leftmost) position where $ a $ and $ b $ differ, the sequence $ a $ has a smaller element than the corresponding element in $ b $ .

输入输出格式

输入格式

The first line contains an integer $ n $ ( $ 1 \le n \le 10^6 $ ) — the number of water tanks. The second line contains $ n $ integers $ a_1, a_2, \dots, a_n $ ( $ 1 \le a_i \le 10^6 $ ) — initial volumes of water in the water tanks, in liters. Because of large input, reading input as doubles is not recommended.

输出格式

Print the lexicographically smallest sequence you can get. In the $ i $ -th line print the final volume of water in the $ i $ -th tank. Your answer is considered correct if the absolute or relative error of each $ a_i $ does not exceed $ 10^{-9} $ . Formally, let your answer be $ a_1, a_2, \dots, a_n $ , and the jury's answer be $ b_1, b_2, \dots, b_n $ . Your answer is accepted if and only if $ \frac{|a_i - b_i|}{\max{(1, |b_i|)}} \le 10^{-9} $ for each $ i $ .

输入输出样例

输入样例 #1

4
7 5 5 7

输出样例 #1

5.666666667
5.666666667
5.666666667
7.000000000

输入样例 #2

5
7 8 8 10 12

输出样例 #2

7.000000000
8.000000000
8.000000000
10.000000000
12.000000000

输入样例 #3

10
3 9 5 5 1 7 5 3 8 7

输出样例 #3

3.000000000
5.000000000
5.000000000
5.000000000
5.000000000
5.000000000
5.000000000
5.000000000
7.500000000
7.500000000

说明

In the first sample, you can get the sequence by applying the operation for subsegment $ [1, 3] $ . In the second sample, you can't get any lexicographically smaller sequence.