Φ²

Sunah is studying a certain microorganism. While researching it, Sunah found that when several of these microorganisms are arranged in a line, they absorb each other according to the following rules until only one remains.

1. Once per day, starting from the microorganism at the front of the line, each microorganism in turn absorbs all adjacent microorganisms that are smaller than or equal to its own size. When it absorbs another microorganism, its size increases by the size of the absorbed one.
2. An absorbed microorganism disappears and cannot act. For example, if there are three microorganisms with sizes $3$, $2$, and $1$, then $2$ is absorbed by $3$ before its turn comes, so after one day the remaining sizes are $5$ and $1$.
3. A microorganism absorbs everything it will absorb that day in a single action. For example, if there are three microorganisms with sizes $3$, $4$, and $5$, and it is $4$'s turn, then $4$ absorbs only $3$. It is impossible for $4$ to absorb $5$ the same day after becoming $7$. So after one day the remaining sizes are $7$ and $5$.

The first line contains the number of microorganisms $N$. ($1\le N\le 500\,000$)

The second line contains $N$ integers $a_1,a_2,\ldots,a_N$ separated by spaces, where $a_i$ is the initial size of the $i$-th microorganism. Each initial size is an integer from $1$ to $N$, inclusive. No two microorganisms have the same initial size.

Print the final size of the microorganism that remains at the end on the first line.

Print the initial position of that microorganism on the second line.