Bob is playing a game, in which he has to fight monsters and he gains XP powers from them. Bob has special spells and he can use them as much as he want while he is still in the game.

The game has $N$ monsters, and each monster's power is less or equal than $10000.$ The monsters powers will be given in array $P$ of size $N,$ where the value $P[$i$]$ denotes the power of monster with index $i.$

At the beginning of the game, Bob starts with monster numbered $1$ and the game ends when Bob kills all the monsters$($all till the $N^{th}$ monster$).$

Bob is currently fighting monster with index i and in one operation he can:

Kill this monster and move to the next one and not earn any XP powers.

Use the spell to kill all the next $J$ monsters including monster $i,$ for all $AJB,AB,B-A500,$ and gain XP power equal to the difference between the power of the strongest monster and the power of the weakest monster $($ maxP$[i]-)$ in range $i,i+J-1$ and move to the monster whose index is $i+J.$

Find the maximum possible XP powers that Bob can gain by using the spells optimally.