"HearthStone" is an online digital collectible card game developed and published by Blizzard Entertainment.

In the game, players have to summon minions and cast spells to attack their opponent.

The following 5 paragraphs illustrate the rules that you need to know in order to solve this problem.

Each minion has its attack value and its hitpoint value.

When a minion receives damage, its hitpoint value decreases by the damage value.

Whenever a minion has a non-positive hitpoint value, it dies.

Minions can have "Deathrattle($$$x$$$/$$$y$$$)" properties, that is, when this minion dies, another minion with $$$x$$$ attack and $$$y$$$ hitpoint will be summoned instantly. Additionally, the summoned minion does not have any "Deathrattle" property.

"Defile" is a spell. When cast, the spell will deal $$$1$$$ damage to all minions, and if any minion dies, the spell will be automatically cast again.

Grammy is a famous player who ranked top $$$10^9$$$ among all "HearthStone" players. Nonetheless, she is unhappy because she does not know how to use "defile" just like the textbook. She wants to do some practice.

$$$n$$$ minions have been placed on the battlefield. The $$$i$$$-th of them have $$$0$$$ attack, $$$10^9$$$ hitpoint, and "Deathrattle($$$i$$$/$$$i$$$)". Grammy can modify each minion's hitpoint to another positive value before she cast the last "Defile" in her hand, can you help her to find out a way to modify each minion's hitpoint so that the recasting effect of the spell will be triggered $$$2n$$$ times? In other words, the spell is cast $$$2n+1$$$ times in total, manually or automatically.