Two Alpinists

AtCoder

IDcodefestival_2016_qualC_c

Time2000ms

Memory256MB

Difficulty—

Mountaineers Mr. Takahashi and Mr. Aoki recently trekked across a certain famous mountain range. The mountain range consists of $N$ mountains, extending from west to east in a straight line as Mt. $1$, Mt. $2$, ..., Mt. $N$. Mr. Takahashi traversed the range from the west and Mr. Aoki from the east. The height of Mt. $i$ is $h_i$, but they have forgotten the value of each $h_i$. Instead, for each $i$ ($1 ≤ i ≤ N$), they recorded the maximum height of the mountains climbed up to the time they reached the peak of Mt. $i$ (including Mt. $i$). Mr. Takahashi's record is $T_i$ and Mr. Aoki's record is $A_i$. We know that the height of each mountain $h_i$ is a positive integer. Compute the number of the possible sequences of the mountains' heights, modulo $10^9 + 7$. Note that the records may be incorrect and thus there may be no possible sequence of the mountains' heights. In such a case, output $0$. ## Constraints * $1 ≤ N ≤ 10^5$ * $1 ≤ T_i ≤ 10^9$ * $1 ≤ A_i ≤ 10^9$ * $T_i ≤ T_{i+1}$ ($1 ≤ i ≤ N - 1$) * $A_i ≥ A_{i+1}$ ($1 ≤ i ≤ N - 1$) ## Input The input is given from Standard Input in the following format: $N$ $T_1$ $T_2$ $...$ $T_N$ $A_1$ $A_2$ $...$ $A_N$ [samples]

Samples

Input #1

5
1 3 3 3 3
3 3 2 2 2

Output #1

4

The possible sequences of the mountains' heights are:

*   $1, 3, 2, 2, 2$
*   $1, 3, 2, 1, 2$
*   $1, 3, 1, 2, 2$
*   $1, 3, 1, 1, 2$

for a total of four sequences.

Input #2

5
1 1 1 2 2
3 2 1 1 1

Output #2

0

The records are contradictory, since Mr. Takahashi recorded $2$ as the highest peak after climbing all the mountains but Mr. Aoki recorded $3$.

Input #3

10
1 3776 3776 8848 8848 8848 8848 8848 8848 8848
8848 8848 8848 8848 8848 8848 8848 8848 3776 5

Output #3

884111967

Don't forget to compute the number modulo $10^9 + 7$.

Input #4

1
17
17

Output #4

1

Some mountain ranges consist of only one mountain.

API Response (JSON)

{
  "problem": {
    "name": "Two Alpinists",
    "description": {
      "content": "Mountaineers Mr. Takahashi and Mr. Aoki recently trekked across a certain famous mountain range. The mountain range consists of $N$ mountains, extending from west to east in a straight line as Mt. $1$",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "codefestival_2016_qualC_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Mountaineers Mr. Takahashi and Mr. Aoki recently trekked across a certain famous mountain range. The mountain range consists of $N$ mountains, extending from west to east in a straight line as Mt. $1$...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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