+ Time limit: 1 second + Memory limit: 256 megabytes ------------- Amirhosein has $n$ seconds available to do his daily activities. He also has $c$ units of money and can tolerate a maximum temperature of $h$ degrees; that is, his body temperature must never exceed $h$. We also know that his body temperature is always a non-negative integer. In each second, Amirhosein chooses one of the following two states: + **Headphones on:** In this state, he can turn the air conditioner on or off. If the air conditioner is off, his over-ear headphones act like a blanket, and his body temperature increases by one degree during that second. If the air conditioner is on, his body temperature does not change. Keeping the air conditioner on for one second costs one unit of money. + **Headphones off:** In this state, his body temperature decreases by one degree during that second, and whether the air conditioner is on or off has no effect on his body temperature; with the exception that the temperature can never become less than zero. More precisely, if the temperature before this second is $t$, then after it, the temperature becomes $max(0, t - 1)$. Amirhosein initially has a body temperature of $0$ degrees, and at no point can his temperature exceed $h$ degrees. Also, the total cost of keeping the air conditioner on during all $n$ seconds must not exceed $c$. Amirhosein's enjoyment from listening to music is calculated as follows: Every **maximal interval** of consecutive seconds during which Amirhosein wears his headphones is considered a music-listening interval. If the length of this interval is $l$ seconds, then $l^2$ is added to his enjoyment. Given the values of $n$, $c$, and $h$, **calculate the maximum amount of enjoyment that Amirhosein can obtain.** # Input The only line of input contains three integers $n$, $h$, and $c$. $$1 \leq n, h, c \leq 10^9$$ # Output Print a single integer equal to the maximum amount of enjoyment that Amirhosein can obtain. # Sample ## Sample input 1 ``` 10 2 2 ``` ## Sample output 1 ``` 21 ``` + $2$ seconds of listening, enjoyment $4$ + $2$ seconds of resting until the temperature reaches zero + $1$ second of listening, enjoyment $1$ + $1$ second of resting + $4$ seconds of listening using $2$ units of money for the air conditioner, enjoyment $16$ In total: $$4 + 1 + 16 = 21$$