题库-CF|【Codeforces Round 263 (Div 2)C】【贪心 哈弗曼思维】Appleman and Toastman 每个非1size子树延展为2子树的最大权
Appleman and Toastman time limit per test
2 seconds memory limit per test
256 megabytes input
standard input output
standard output 【题库-CF|【Codeforces Round 263 (Div 2)C】【贪心 哈弗曼思维】Appleman and Toastman 每个非1size子树延展为2子树的最大权】 Appleman and Toastman play a game. Initially Appleman gives one group of n numbers to the Toastman, then they start to complete the following tasks:
- Each time Toastman gets a group of numbers, he sums up all the numbers and adds this sum to the score. Then he gives the group to the Appleman.
- Each time Appleman gets a group consisting of a single number, he throws this group out. Each time Appleman gets a group consisting of more than one number, he splits the group into two non-empty groups (he can do it in any way) and gives each of them to Toastman.
Input The first line contains a single integer n (1?≤?n?≤?3·105). The second line contains n integers a1, a2, ..., an (1?≤?ai?≤?106) — the initial group that is given to Toastman.
Output Print a single integer — the largest possible score.
Examples input
3 3 1 5
output
26
input
1 10
output
10
Note Consider the following situation in the first example. Initially Toastman gets group [3, 1, 5] and adds 9 to the score, then he give the group to Appleman. Appleman splits group [3, 1, 5] into two groups: [3, 5] and [1]. Both of them should be given to Toastman. When Toastman receives group [1], he adds 1 to score and gives the group to Appleman (he will throw it out). When Toastman receives group [3, 5], he adds 8 to the score and gives the group to Appleman. Appleman splits [3, 5] in the only possible way: [5] and [3]. Then he gives both groups to Toastman. When Toastman receives [5], he adds 5 to the score and gives the group to Appleman (he will throws it out). When Toastman receives [3], he adds 3 to the score and gives the group to Appleman (he will throws it out). Finally Toastman have added 9 + 1 + 8 + 5 + 3 = 26 to the score. This is the optimal sequence of actions.
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