Richard has quit competitive programming and has opened an ice cream stand. Help him run his stand! Here are the operations to support:

ADD K P - Richard is now willing to sell ~K~ more ice cream cones, each at ~P~ dollars.

ADDRANGE A B - Richard is now willing to sell one more ice cream cone for each price ~P~ between ~A~ and ~B~, inclusive.

BUYAMT Q - Nick has ~Q~ dollars, and buys the maximum number of cones he can, starting from cheapest to most expensive. Report how many cones Nick buys.

BUYLOW L - Nick buys the ~L~ cheapest cones Richard is selling, or all of them if Richard is selling fewer than ~L~ of them. Report the total cost of the cones bought.

BUYHIGH L - Nick buys the ~L~ most expensive cones Richard is selling, or all of them if Richard is selling fewer than ~L~ of them. Report the total cost of the cones bought.

COST L - Report the cost of the ~L~th cheapest cone. If there are fewer than ~L~ cones, return -1.

NUMCONES - Report how many cones Richard is currently selling.

TOTALCOST - Report the total cost of every cone that Richard is currently selling.

Constraints

For 2 marks, ~N \le 100~.

For 3 additional marks, there will be no BUYLOW, BUYHIGH, or COST operations.

For 4 additional marks, there will be no COST operations.

Input Specification

The first line will contain a single positive integer ~N~, the number of operations to support. ~N~ will be at most ~3 \cdot 10^5~.

Each of the next ~N~ lines will contain information for one of the operations, as shown above.

As written above, ~0 < K, P \le 2 \cdot 10^6~, ~0 < A \le B \le 2 \cdot 10^6~, ~0 < L \le 10^{12}~, and ~0 < Q \le 10^{18}~.

Output Specification

For every operation that demands reporting a value, print out the desired value.

Sample Input

8
ADD 5 4
ADDRANGE 1 7
BUYAMT 3
BUYLOW 2
BUYHIGH 2
COST 1
NUMCONES
TOTALCOST

Sample Output

2
7
13
4
6
25