Sage's Birthday (hard version)

题意翻译

Sage的生日去商店买东西，有 $ n $ 件商品排成一行，每个商品都有一个价格 $ a_i $ （商品价格可能相同）。Sage只会买价格比左右两边商品价格都严格低的商品（他不会买最左边和最右边的商品）。 问最多能让Sage买几件商品？第一行输出最多能买的商品的数量，第二行输出一种方案。

题目描述

This is the hard version of the problem. The difference between the versions is that in the easy version all prices $ a_i $ are different. You can make hacks if and only if you solved both versions of the problem. Today is Sage's birthday, and she will go shopping to buy ice spheres. All $ n $ ice spheres are placed in a row and they are numbered from $ 1 $ to $ n $ from left to right. Each ice sphere has a positive integer price. In this version, some prices can be equal. An ice sphere is cheap if it costs strictly less than two neighboring ice spheres: the nearest to the left and the nearest to the right. The leftmost and the rightmost ice spheres are not cheap. Sage will choose all cheap ice spheres and then buy only them. You can visit the shop before Sage and reorder the ice spheres as you wish. Find out the maximum number of ice spheres that Sage can buy, and show how the ice spheres should be reordered.

输入输出格式

输入格式

The first line contains a single integer $ n $ $ (1 \le n \le 10^5) $ — the number of ice spheres in the shop. The second line contains $ n $ integers $ a_1, a_2, \dots, a_n $ $ (1 \le a_i \le 10^9) $ — the prices of ice spheres.

输出格式

In the first line print the maximum number of ice spheres that Sage can buy. In the second line print the prices of ice spheres in the optimal order. If there are several correct answers, you can print any of them.

输入输出样例

输入样例 #1

7
1 3 2 2 4 5 4

输出样例 #1

3
3 1 4 2 4 2 5

说明

In the sample it's not possible to place the ice spheres in any order so that Sage would buy $ 4 $ of them. If the spheres are placed in the order $ (3, 1, 4, 2, 4, 2, 5) $ , then Sage will buy one sphere for $ 1 $ and two spheres for $ 2 $ each.