Holi at Kashmere Gate

On the occasion of Holi, the residents of Kashmere Gate have decided that they will paint their houses in either Pink, Orange or Yellow color and not other. They have also decided that no two adjacent houses will have the same color. For house i, i-1 and i+1 are the neighbors and note that the first and the last house are not neighbors. The cost of painting a house in a particular color is diff