Problem: Pasha decided to invite his friends to a tea party. For that occasion, he has a large teapot with the capacity of w milliliters and 2n tea cups, each cup is for one of Pasha's friends. The i-th cup can hold at most ai milliliters of water.

It turned out that among Pasha's friends there are exactly n boys and exactly n girls and all of them are going to come to the tea party. To please everyone, Pasha decided to pour the water for the tea as follows:

  * Pasha can boil the teapot exactly once by pouring there at most w milliliters of water; 
  * Pasha pours the same amount of water to each girl; 
  * Pasha pours the same amount of water to each boy; 
  * if each girl gets x milliliters of water, then each boy gets 2x milliliters of water. 



In the other words, each boy should get two times more water than each girl does.

Pasha is very kind and polite, so he wants to maximize the total amount of the water that he pours to his friends. Your task is to help him and determine the optimum distribution of cups between Pasha's friends.

Input

The first line of the input contains two integers, n and w (1 ≤ n ≤ 105, 1 ≤ w ≤ 109) — the number of Pasha's friends that are boys (equal to the number of Pasha's friends that are girls) and the capacity of Pasha's teapot in milliliters.

The second line of the input contains the sequence of integers ai (1 ≤ ai ≤ 109, 1 ≤ i ≤ 2n) — the capacities of Pasha's tea cups in milliliters.

Output

Print a single real number — the maximum total amount of water in milliliters that Pasha can pour to his friends without violating the given conditions. Your answer will be considered correct if its absolute or relative error doesn't exceed 10 - 6.

Examples

Input

2 4
1 1 1 1


Output

3

Input

3 18
4 4 4 2 2 2


Output

18

Input

1 5
2 3


Output

4.5

Note

Pasha also has candies that he is going to give to girls but that is another task...

Solution (in PYTHON3):

Solution:
#!/usr/bin/env python
# 557B_tea.py - Codeforces.com 557B Tea quiz
#
# Copyright (C) 2015 Sergey
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#       http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.

"""
Input

The first line of the input contains two integers, n and w
the number of Pasha's friends that are boys (equal to the number of Pasha's
friends that are girls) and the capacity of Pasha's teapot in milliliters.

The second line of the input contains the sequence of integers ai
the capacities of Pasha's tea cups in milliliters.

Output

Print a single real number the maximum total amount of water in milliliters
that Pasha can pour to his friends without violating the given conditions.
Your answer will be considered correct if its absolute or relative error
doesn't exceed 10-6.
"""

# Standard libraries
import unittest
import sys
import re

# Additional libraries


###############################################################################
# Tea Class
###############################################################################


class Tea:
    """ Tea representation """

    def __init__(self, args):
        """ Default constructor """

        self.list = args[2]
        self.n = args[0]
        self.w = args[1]

        self.slist = sorted(self.list)

        self.b = self.slist[self.n]
        self.g = self.slist[0]

        self.wmax = (
            self.n * min(self.b, self.g * 2) + self.n * min(self.b/2, self.g))

    def calculate(self):
        """ Main calcualtion function of the class """

        result = min(self.wmax, self.w)

        return str(result)


###############################################################################
# Executable code
###############################################################################


def get_inputs(test_inputs=None):

    it = iter(test_inputs.split("\n")) if test_inputs else None

    def uinput():
        """ Unit-testable input function wrapper """
        if it:
            return next(it)
        else:
            return input()

    # Getting string inputs. Place all uinput() calls here
    nums = [int(s) for s in uinput().split()]
    cups = [int(s) for s in uinput().split()]

    # Decoding inputs into a list
    inputs = nums
    inputs.append(cups)

    return inputs


def calculate(test_inputs=None):
    """ Base class calculate method wrapper """
    return Tea(get_inputs(test_inputs)).calculate()


###############################################################################
# Unit Tests
###############################################################################


class unitTests(unittest.TestCase):

    def test_sample_tests(self):
        """ Quiz sample tests. Add \n to separate lines """

        # Sample test 1
        test = "2 4\n1 1 1 1"
        self.assertEqual(calculate(test), "3.0")
        self.assertEqual(get_inputs(test), [2, 4, [1, 1, 1, 1]])

        # Other tests
        test = "3 18\n4 4 4 2 2 2"
        self.assertEqual(calculate(test), "18.0")
        test = "1 5\n2 3"
        self.assertEqual(calculate(test), "4.5")

        test = "2 5\n1 2 3 4"
        self.assertEqual(calculate(test), "5")

    def test_Tea_class__basic_functions(self):
        """ Tea class basic functions testing """

        # Constructor test
        d = Tea([2, 4, [1, 1, 2, 1]])
        self.assertEqual(d.list[0], 1)
        self.assertEqual(d.w, 4)
        self.assertEqual(d.n, 2)

        # Sort cups
        self.assertEqual(d.slist[-1], 2)
        self.assertEqual(d.b, 1)
        self.assertEqual(d.g, 1)

        self.assertEqual(d.wmax, 3)

if __name__ == "__main__":

    # Avoiding recursion limitaions
    sys.setrecursionlimit(100000)

    if sys.argv[-1] == "-ut":
        unittest.main(argv=[" "])

    # Print the result string
    print(calculate())