In easier times, Farmer John's cows had no problems. These days, though, they have problems, lots of problems; they have P (1 ≤ P ≤ 300) problems, to be exact. They have quit providing milk and have taken regular jobs like all other good citizens. In fact, on a normal month they make M (1 ≤ M ≤ 1000) money.

Their problems, however, are so complex they must hire consultants to solve them. Consultants are not free, but they are competent: consultants can solve any problem in a single month. Each consultant demands two payments: one in advance (1 ≤ payment ≤ M) to be paid at the start of the month problem-solving is commenced and one more payment at the start of the month after the problem is solved (1 ≤ payment ≤ M). Thus, each month the cows can spend the money earned during the previous month to pay for consultants. Cows are spendthrifts: they can never save any money from month-to-month; money not used is wasted on cow candy.

Since the problems to be solved depend on each other, they must be solved mostly in order. For example, problem 3 must be solved before problem 4 or during the same month as problem 4.

Determine the number of months it takes to solve all of the cows' problems and pay for the solutions.

+------+-------+--------+---------+---------+--------+
|      | Avail | Probs  | Before  | After   | Candy  |
|Month | Money | Solved | Payment | Payment | Money  |
+------+-------+--------+---------+---------+--------+
| 1    | 0     | -none- | 0       | 0       | 0      |
| 2    | 100   | 1, 2   | 40+60   | 0       | 0      |
| 3    | 100   | 3, 4   | 30+30   | 20+20   | 0      |
| 4    | 100   | -none- | 0       | 50+50   | 0      |
| 5    | 100   | 5      | 40      | 0       | 60     |
| 6    | 100   | -none- | 0       | 40      | 60     | 
+------+-------+--------+---------+---------+--------+