You have planned some train traveling one year in advance. The days of the year in which you will travel are given as an integer array days. Each day is an integer from 1 to 365.

Train tickets are sold in three different ways:

• a 1-day pass is sold for costs[0] dollars,
• a 7-day pass is sold for costs[1] dollars, and
• a 30-day pass is sold for costs[2] dollars.

The passes allow that many days of consecutive travel.

• For example, if we get a 7-day pass on day 2, then we can travel for 7 days: 2, 3, 4, 5, 6, 7, and 8.

Return the minimum number of dollars you need to travel every day in the given list of days.

Example

Input: days = [1,4,6,7,8,20], costs = [2,7,15]
Output: 11
Explanation: For example, here is one way to buy passes that lets you travel your travel plan:
On day 1, you bought a 1-day pass for costs[0] = $2, which covered day 1.
On day 3, you bought a 7-day pass for costs[1] = $7, which covered days 3, 4, ..., 9.
On day 20, you bought a 1-day pass for costs[0] = $2, which covered day 20.
In total, you spent $11 and covered all the days of your travel.

Solution

/**
 * @param {number[]} days
 * @param {number[]} costs
 * @return {number}
 */
var mincostTickets = function (days, costs) {
  //Array to store the minimum cost for each day
  let dp = new Array(366).fill(0);

  // Set of days where we need to travel
  let travelDays = new Set(days);

  for (let i = 1; i < dp.length; i++) {
    //If we don't need to travel on this day, the cost is the same as the previous day
    if (!travelDays.has(i)) {
      dp[i] = dp[i - 1];
    } else {
      //Otherwise, the cost is the minimum of the cost of the previous day, the cost of 7 days ago, or the cost of 30 days ago
      dp[i] = Math.min(
        dp[i - 1] + costs[0],
        dp[Math.max(0, i - 7)] + costs[1],
        dp[Math.max(0, i - 30)] + costs[2]
      );
    }
  }
  //Return the cost for the last day
  return dp[dp.length - 1];
};