The Price Is Right is a television game show. In the final round of competition, the contestant is shown the prizes which he can win. To win everything, he must make an educated guess and arrange the prizes in increasing order of price.
Once the contestant has completed ordering prizes, the host begins to reveal the price of each prize in any order that he wishes. To make the show more interesting however, the host reveals prices in such a way that as many prices are revealed as possible before an error in the order is revealed.
Each element in prices represents the price of a prize. The order of prices represents what the contestant thought the order was when arranging prices.
Given a int[] of prices as ordered by the contestant, return a int[] with two elements. The first element should be the maximum possible number of prices revealed before the order of prices is broken, while the second element should be the total number of ways of achieving that maximum number.
For example, prices = {30, 10, 20, 40, 50}
The host could reveal the following prices: 30 * * 40 50. The next price revealed (either 10 or 20) will cause an error in the ordering to be revealed. In this case, 3 prices were revealed. Alternatively, the host could reveal the following prices: * 10 20 40 50. Once again, the next price revealed will cause an error in the ordering to be revealed. However, in this case, 4 prices were revealed and thus the host would prefer to reveal the prices this way. Note that there is only 1 way of revealing 4 prices. The method should return {4,1}.
