Happy new 2015 Year !!!!

Calculus Level 5

What is the infimum(minimum) value of a1a2+a3++a2015+a2a1+a3++a2015++a2014a1+a2++a2013+a2015+a2015a1+a2++a2013+a2014?\sqrt { \frac { { a }_{ 1 } }{ { a }_{ 2 }+{ a }_{ 3\quad }+\ldots +{ a }_{ 2015 } } } +\sqrt { \frac { { a }_{ 2 } }{ { a }_{ 1 }+{ a }_{ 3 }+\ldots +{ a }_{ 2015 } } } +\ldots + \\ \sqrt { \frac { { a }_{ 2014 } }{ { a }_{ 1 }+{ a }_{ 2 }+\ldots +{ a }_{ 2013 }+{ a }_{ 2015 } } } +\sqrt { \frac { { a }_{ 2015 } }{ { a }_{ 1 }+{ a }_{ 2 }+\ldots+{ a }_{ 2013 }+{ a }_{ 2014 } } } ?

Details and assumptions:
- a1,a2,...,a2014,a2015{ a }_{ 1 }, { a }_{ 2 }, ... , { a }_{ 2014 }, { a }_{ 2015 } are positive real numbers!
- Enter your answer to two decimals!
- This problem was inspired by "2015 is coming!!!!" by Martin Nikolov!

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