Peddler

AtCoder

IDabc188_e

Time2000ms

Memory256MB

Difficulty—

In Takahashi Kingdom, there are $N$ towns, called Town $1$ through Town $N$. There are also $M$ roads in the kingdom, called Road $1$ through Road $M$. By traversing Road $i$, you can travel from Town $X_i$ to Town $Y_i$, but not vice versa. Here, it is guaranteed that $X_i < Y_i$. Gold is actively traded in this kingdom. At Town $i$, you can buy or sell $1$ kilogram of gold for $A_i$ yen (the currency of Japan). Takahashi, a traveling salesman, plans to buy $1$ kilogram of gold at some town, traverse one or more roads, and sell $1$ kilogram of gold at another town. Find the maximum possible profit (that is, the selling price minus the buying price) in this plan. ## Constraints * $2 \le N \le 2 \times 10^5$ * $1 \le M \le 2 \times 10^5$ * $1 \le A_i \le 10^9$ * $1 \le X_i \lt Y_i \le N$ * $(X_i, Y_i) \neq (X_j, Y_j) (i \neq j)$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $M$ $A_1$ $A_2$ $A_3$ $\dots$ $A_N$ $X_1$ $Y_1$ $X_2$ $Y_2$ $X_3$ $Y_3$ $\hspace{15pt} \vdots$ $X_M$ $Y_M$ [samples]

Samples

Input #1

Output #1

3

We can achieve the profit of $3$ yen, as follows:

*   At Town $1$, buy one kilogram of gold for $2$ yen.
*   Traverse Road $2$ to get to Town $2$.
*   Traverse Road $1$ to get to Town $4$.
*   At Town $4$, sell one kilogram of gold for $5$ yen.

Input #2

5 5
13 8 3 15 18
2 4
1 2
4 5
2 3
1 3

Output #2

10

We can achieve the profit of $10$ yen, as follows:

*   At Town $2$, buy one kilogram of gold for $8$ yen.
*   Traverse Road $1$ to get to Town $4$.
*   Traverse Road $3$ to get to Town $5$.
*   At Town $5$, sell one kilogram of gold for $18$ yen.

Input #3

3 1
1 100 1
2 3

Output #3

\-99

Note that we cannot sell gold at the town where we bought the gold, which means the answer may be negative.

API Response (JSON)

{
  "problem": {
    "name": "Peddler",
    "description": {
      "content": "In Takahashi Kingdom, there are $N$ towns, called Town $1$ through Town $N$.   There are also $M$ roads in the kingdom, called Road $1$ through Road $M$. By traversing Road $i$, you can travel from To",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc188_e"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "In Takahashi Kingdom, there are $N$ towns, called Town $1$ through Town $N$.  \nThere are also $M$ roads in the kingdom, called Road $1$ through Road $M$. By traversing Road $i$, you can travel from To...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments