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There is an island far away occupied by a tribe. Among people in this tribe, $n$ eye colors occur: there are $a_i$ people with the eye color $i$ ($a_i > 0$), and there are no other colors known to the tribe. More formally, the members of the tribe know the value of $n$, but they don't know that all eye colors actually occur (that all $a_i > 0$). The tribe follows a specific religion: if someone can deduce their own eye color, they commit suicide the next day. It must be said, the people in the tribe are incredibly smart.
Once, at day 0, a traveler arrives to the island, meets the tribe and says $n$ true sentences, in which $b_i \ge 0$, and at least one $b_i > 0$:
Find the last day when the suicides will take place and the total number of people committed suicide.
The first line contains an integer $n$ ($2 \le n \le 200000$) --- the number of eye colors.
Each of the next $n$ lines contains two integers $a_i$ and $b_i$ ($1 \le a_i \le 10^9, 0 \le b_i \le a_i$, at least one $b_i > 0$) --- the number of people with the eye color $i$ and the lower bound of this number said by the traveler.
Output two integers --- the number of the last day when the suicides will take place, and the total number of people committed suicide.
2 1 1 3 0
2 3 1 1 0
3 3 1 1 0 1 0
Let's show what happens in the first sample.
The person with the eye color $1$ doesn't see anyone with the eye color $1$ around, but hears that there is at least one person with this color. So they deduce who can be this person and commit suicide at the day $1$.
All other people know that only two colors occur and that one person with the eye color $1$ is dead. So they deduce all of them have eye color $2$ and commit suicide at the day $2$.