As winter approached, a prince wanted to see his future kingdom. He decided to disguise his appearance and venture into the realm. To discover the character of the people, he gave away gold coins. Soon after he left, he met a small boy. The prince gave him one-fourth of his coins plus two more. A few days later, the prince saw an old man leaning on a tree. The prince had compassion on him and also gave him one-fourth of his remaining coins plus two more. Finally, the prince saw some youth. He gave them one-fourth of his remaining coins plus two more. At the end of the next day, the prince returned to the castle with only 4 coins left in his bag. How many coins did the prince initially have in his bag? Show your work.;