The province has the Monte Cristi and Valverde provinces to the north , the Santiago province to the east , the San Juan and ElÃ as PiÃ a provinces to the south and the DajabÃ n province to the west . The Santiago RodrÃ guez province has the Monte Cristi and Valverde provinces to the north , the Santiago province to the east , the San Juan and ElÃ as PiÃ a provinces to the south and the DajabÃ n province to the west .