Gregor is a salesperson employed in the city of Cartesia, which lies on an infinite plane. The locations of retailers follow the Cartesian coordinate system.

There are N + 1 retailers in the city:

• N retailers, with positions 1 to N, have coordinates: [ (X_1, 0), (X_2, 0), \ldots, (X_N, 0) ] i.e., all these retailers lie on the X-axis.
• The head retailer, with position N + 1, is located at: [ (X_{N+1}, Y_{N+1}) ]

Gregor wants to find the shortest possible path starting from the K-th retailer and visiting all the other retailers exactly once. He may visit the head retailer twice during the route.

The distance between two retailers is the Euclidean distance between their corresponding Cartesian coordinates.

Print the minimum possible path length, rounded to 6 decimal places.

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Function Description

double minPossLen(
    int posK,
    vector<int> retailerXCoord,
    int headXCoord,
    int headYCoord
);

Parameters

• posK – Position (1-indexed) of the starting retailer.
• retailerXCoord – List containing the X-coordinates of the N retailers on the X-axis.
• headXCoord – X-coordinate of the head retailer.
• headYCoord – Y-coordinate of the head retailer.

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Input Format

1. Integer posK – starting retailer position.
2. Integer num – number of retailers on the X-axis.
3. num space-separated integers – X-coordinates of the retailers.
4. Integer headXCoord.
5. Integer headYCoord.

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Output Format

Print a single floating-point number representing the minimum possible path length, rounded to 6 decimal places.

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Constraints

• (1 \le \text{posK} \le \text{num} + 1)

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Example

Input

1
3
0 1 2
1
1

Output

3.828427

Explanation

• Retailers are located at:

  • (0, 0)
  • (1, 0)
  • (2, 0)

• Head retailer is at:

  • (1, 1)

• Starting retailer:

  • (0, 0)

One minimum path is:

(0,0) → (1,1) → (0,0) → (1,0) → (2,0)

Path length:

√2 + √2 + 1 + 1
= 1.4142135 + 1.4142135 + 1 + 1
= 3.828427

Hence, the minimum possible path length is:

3.828427