Poker Hands S

题面翻译

Bessie 有 $n$ 堆牌，每堆牌有 $a_i$ 张。她一次可以将第 $i$ 堆到第 $j$ 堆里打一张出去，求打完 $n$ 堆牌最少的次数。

对于 $100\%$ 的数据，$1\le n\le10^5,0\le a_i\le10^5$。

题目描述

Bessie and her friends are playing a unique version of poker involving a deck with N (1 <= N <= 100,000) different ranks, conveniently numbered 1..N (a normal deck has N = 13). In this game, there is only one type of hand the cows can play: one may choose a card labeled i and a card labeled j and play one card of every value from i to j. This type of hand is called a "straight".

Bessie's hand currently holds $a_i$ cards of rank i (0 <= $a_i$ <= 100000). Help her find the minimum number of hands she must play to get rid of all her cards.

Bessie和她的朋友们正在玩一种独特的扑克游戏，游戏中的牌组有 N (1 <= N <= 100,000) 个不同的点数，编号为 1 到 N（普通牌组的 N = 13）。在这个游戏中，奶牛只能打出一种牌型：可以选择一张标有 i 的牌和一张标有 j 的牌，然后从 i 到 j 的每个点数都打出一张。这种牌型被称为“顺子”。

贝西手中目前有 $a_i$ 张点数为 i 的牌（0 <= $a_i$ <= 100,000）。请帮她算出至少需要打多少手牌才能打出所有牌。

输入格式

* Line 1: The integer N. * 第 1 行：整数 N。

* Lines 2..1+N: Line i+1 contains the value of $a_i$. * 1+N：第 i+1 行包含 $a_i$ 的值

输出格式

* Line 1: The minimum number of straights Bessie must play to get rid of all her cards.

样例 #1

样例输入 #1

5 
2 
4 
1 
2 
3

样例输出 #1

6

提示

Bessie can play a straight from 1 to 5, a straight from 1 to 2, a straight from 4 to 5, two straights from 2 to 2, and a straight from 5 to 5, for a total of 6 rounds necessary to get rid of all her cards.

大致意思： Bessie可以打出 1 到 5 的顺子、1 到 2 的顺子、4 到 5 的顺子、2 到 2 的两张顺子以及 5 到 5 的顺子，总共需要 6 轮才能打出所有牌。