Ex - Monster

AtCoder

IDabc275_h

Time2000ms

Memory256MB

Difficulty—

There are $N$ monsters along a number line. At the coordinate $i$ $(1\leq i\leq N)$ is a monster with a stamina of $A_i$. Additionally, at the coordinate $i$, there is a permanent shield of a strength $B_i$. This shield persists even when the monster at the same coordinate has a health of $0$ or below. Takahashi, a magician, can perform the following operation any number of times. * Choose integers $l$ and $r$ satisfying $1\leq l\leq r\leq N$. * Then, consume $\max(B_l, B_{l+1}, \ldots, B_r)$ MP (magic points) to decrease by $1$ the stamina of each of the monsters at the coordinates $l,l+1,\ldots,r$. When choosing $l$ and $r$, it is fine if some of the monsters at the coordinates $l,l+1,\ldots,r$ already have a stamina of $0$ or below. Note, however, that the shields at all those coordinates still exist. Takahashi wants to make the stamina of every monster $0$ or below. Find the minimum total MP needed to achieve his objective. ## Constraints * $1 \leq N \leq 10^5$ * $1 \leq A_i,B_i \leq 10^9$ * All values in the input are integers. ## Input The input is given from Standard Input in the following format: $N$ $A_1$ $A_2$ $\ldots$ $A_N$ $B_1$ $B_2$ $\ldots$ $B_N$ [samples]

Samples

Input #1

5
4 3 5 1 2
10 40 20 60 50

Output #1

210

Takahashi can achieve his objective as follows.

*   Choose $(l,r)=(1,5)$. Consume $\max(10,40,20,60,50)=60$ MP, and the staminas of the monsters are $(3,2,4,0,1)$.
*   Choose $(l,r)=(1,5)$. Consume $\max(10,40,20,60,50)=60$ MP, and the staminas of the monsters are $(2,1,3,-1,0)$.
*   Choose $(l,r)=(1,3)$. Consume $\max(10,40,20)=40$ MP, and the staminas of the monsters are $(1,0,2,-1,0)$.
*   Choose $(l,r)=(1,1)$. Consume $\max(10)=10$ MP, and the staminas of the monsters are $(0,0,2,-1,0)$.
*   Choose $(l,r)=(3,3)$. Consume $\max(20)=20$ MP, and the staminas of the monsters are $(0,0,1,-1,0)$.
*   Choose $(l,r)=(3,3)$. Consume $\max(20)=20$ MP, and the staminas of the monsters are $(0,0,0,-1,0)$.

Here, he consumes a total of $60+60+40+10+20+20=210$ MP, which is the minimum possible.

Input #2

1
1000000000
1000000000

Output #2

1000000000000000000

Input #3

10
522 4575 6426 9445 8772 81 3447 629 3497 7202
7775 4325 3982 4784 8417 2156 1932 5902 5728 8537

Output #3

77917796

API Response (JSON)

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    "name": "Ex - Monster",
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      "content": "There are $N$ monsters along a number line. At the coordinate $i$ $(1\\leq i\\leq N)$ is a monster with a stamina of $A_i$.   Additionally, at the coordinate $i$, there is a permanent shield of a streng",
      "description_type": "Markdown"
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    {
      "statement_type": "Markdown",
      "content": "There are $N$ monsters along a number line. At the coordinate $i$ $(1\\leq i\\leq N)$ is a monster with a stamina of $A_i$.  \nAdditionally, at the coordinate $i$, there is a permanent shield of a streng...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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