Contest Duration: ~ (local time) (150 minutes) Back to Home
C - Fountain Walk /

Time Limit: 2 sec / Memory Limit: 256 MB

### 問題文

すべての東西方向の通りは、すべての南北方向の通りと交わります。すべての交差点は、交差する南北方向の通りの番号を x、東西方向の通りの番号を y として組 (x, y) で表されます。

この都市には N 個の噴水があり、交差点 (X_i, Y_i) に設置されています。 通常の交差点と異なり、これらの交差点には交差点を中心とした半径 10 メートルの円が噴水の外周として描かれており、その内部に道路はありません。

### 制約

• 0 \leq x_1, y_1, x_2, y_2 < 10^8
• 1 \leq N \leq 200,000
• 0 \leq X_i, Y_i < 10^8
• i \neq j のとき X_i \neq X_j
• i \neq j のとき Y_i \neq Y_j
• 交差点 (x_1, y_1), (x_2, y_2) は異なり、これらの位置に噴水は設置されていない。
• 入力値はすべて整数である。

### 入力

x_1 y_1 x_2 y_2
N
X_1 Y_1
X_2 Y_2
:
X_N Y_N


### 入力例 1

1 1 6 5
3
3 2
5 3
2 4


### 出力例 1

891.415926535897938


### 入力例 2

3 5 6 4
3
3 2
5 3
2 4


### 出力例 2

400.000000000000000


### 入力例 3

4 2 2 2
3
3 2
5 3
2 4


### 出力例 3

211.415926535897938


Score : 900 points

### Problem Statement

In the city of Nevermore, there are 10^8 streets and 10^8 avenues, both numbered from 0 to 10^8-1. All streets run straight from west to east, and all avenues run straight from south to north. The distance between neighboring streets and between neighboring avenues is exactly 100 meters.

Every street intersects every avenue. Every intersection can be described by pair (x, y), where x is avenue ID and y is street ID.

There are N fountains in the city, situated at intersections (X_i, Y_i). Unlike normal intersections, there's a circle with radius 10 meters centered at the intersection, and there are no road parts inside this circle.

The picture below shows an example of how a part of the city with roads and fountains may look like.

City governors don't like encountering more than one fountain while moving along the same road. Therefore, every street contains at most one fountain on it, as well as every avenue.

Citizens can move along streets, avenues and fountain perimeters. What is the shortest distance one needs to cover in order to get from intersection (x_1, y_1) to intersection (x_2, y_2)?

### Constraints

• 0 \leq x_1, y_1, x_2, y_2 < 10^8
• 1 \leq N \leq 200,000
• 0 \leq X_i, Y_i < 10^8
• X_i \neq X_j for i \neq j
• Y_i \neq Y_j for i \neq j
• Intersections (x_1, y_1) and (x_2, y_2) are different and don't contain fountains.
• All input values are integers.

### Input

Input is given from Standard Input in the following format:

x_1 y_1 x_2 y_2
N
X_1 Y_1
X_2 Y_2
:
X_N Y_N


### Output

Print the shortest possible distance one needs to cover in order to get from intersection (x_1, y_1) to intersection (x_2, y_2), in meters. Your answer will be considered correct if its absolute or relative error doesn't exceed 10^{-11}.

### Sample Input 1

1 1 6 5
3
3 2
5 3
2 4


### Sample Output 1

891.415926535897938


One possible shortest path is shown on the picture below. The path starts at the blue point, finishes at the purple point and follows along the red line.

### Sample Input 2

3 5 6 4
3
3 2
5 3
2 4


### Sample Output 2

400.000000000000000


### Sample Input 3

4 2 2 2
3
3 2
5 3
2 4


### Sample Output 3

211.415926535897938