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luminous jewels, JAVA Programming

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Luminous Jewels - The Polishing Game

Byteland county is very famous for luminous jewels. Luminous jewels are used in making beautiful necklaces. A necklace consists of various luminous jewels of particular colour. Necklaces require polishing the jewels. Operationally, all jewels of the same colour can be polished in one sitting.
Operationally, all jewels of the same colour can be polished in one sitting. Cost of polishing increases with every sitting. Your task is to minimize the cost of polishing the necklace, given following conditions

Jewels can only be removed for polishing from either end of the necklace (i.e. head or tail)
Cost of polishing = Sitting Number * Colour Value of the Luminous Jewel
The necklace is represented as a String and each character of the string is a Luminous Jewel
Similar character is the same Luminous Jewel which has same Colour Value

Colour Value for different Jewels named from a to z are 1 to 26 respectively. For e.g. a = 1, b = 2, ... z = 26.

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