Problem:
Score : 600 points

Problem Statement

There is a function f(x), which is initially a constant function f(x) = 0.

We will ask you to process Q queries in order. There are two kinds of queries, update queries and evaluation queries, as follows:

An update query 1 a b: Given two integers a and b, let g(x) = f(x) + |x - a| + b and replace f(x) with g(x).

An evaluation query 2: Print x that minimizes f(x), and the minimum value of f(x). If there are multiple such values of x, choose the minimum such value.

We can show that the values to be output in an evaluation query are always integers, so we ask you to print those values as integers without decimal points.

Constraints

All values in input are integers.

1 \leq Q \leq 2 \times 10^5

-10^9 \leq a, b \leq 10^9

The first query is an update query.

Input

Input is given from Standard Input in the following format:

Q
Query_1
:
Query_Q

See Sample Input 1 for an example.

Output

For each evaluation query, print a line containing the response, in the order in which the queries are given.

The response to each evaluation query should be the minimum value of x that minimizes f(x), and the minimum value of f(x), in this order, with space in between.

Sample Input 1

4
1 4 2
2
1 1 -8
2

Sample Output 1

4 2
1 -3

In the first evaluation query, f(x) = |x - 4| + 2, which attains the minimum value of 2 at x = 4.

In the second evaluation query, f(x) = |x - 1| + |x - 4| - 6, which attains the minimum value of -3 when 1 \leq x \leq 4. Among the multiple values of x that minimize f(x), we ask you to print the minimum, that is, 1.

Sample Input 2

4
1 -1000000000 1000000000
1 -1000000000 1000000000
1 -1000000000 1000000000
2

Sample Output 2

-1000000000 3000000000

Solution in Rust (1.15.1) (judge verdict: Accepted)

macro_rules ! input { ( source = $ s : expr , $ ( $ r : tt ) * ) => { let mut iter = $ s . split_whitespace ( ) ; input_inner ! { iter , $ ( $ r ) * } } ; ( iter = $ iter : ident , $ ( $ r : tt ) * ) => { let s = { use std :: io :: Read ; let mut s = String :: new ( ) ; std :: io :: stdin ( ) . read_to_string ( & mut s ) . unwrap ( ) ; s } ; let mut $ iter = s . split_whitespace ( ) ; input_inner ! { $ iter , $ ( $ r ) * } } ; ( $ ( $ r : tt ) * ) => { let s = { use std :: io :: Read ; let mut s = String :: new ( ) ; std :: io :: stdin ( ) . read_to_string ( & mut s ) . unwrap ( ) ; s } ; let mut iter = s . split_whitespace ( ) ; input_inner ! { iter , $ ( $ r ) * } } ; }
macro_rules ! input_inner { ( $ iter : expr ) => { } ; ( $ iter : expr , ) => { } ; ( $ iter : expr , mut $ var : ident : $ t : tt $ ( $ r : tt ) * ) => { let mut $ var = read_value ! ( $ iter , $ t ) ; input_inner ! { $ iter $ ( $ r ) * } } ; ( $ iter : expr , mut $ var : ident $ ( $ r : tt ) * ) => { input_inner ! { $ iter , mut $ var : usize $ ( $ r ) * } } ; ( $ iter : expr , $ var : ident : $ t : tt $ ( $ r : tt ) * ) => { let $ var = read_value ! ( $ iter , $ t ) ; input_inner ! { $ iter $ ( $ r ) * } } ; ( $ iter : expr , $ var : ident $ ( $ r : tt ) * ) => { input_inner ! { $ iter , $ var : usize $ ( $ r ) * } } ; }
macro_rules ! read_value { ( $ iter : expr , ( $ ( $ t : tt ) ,* ) ) => { ( $ ( read_value ! ( $ iter , $ t ) ) ,* ) } ; ( $ iter : expr , [ $ t : tt ; $ len : expr ] ) => { ( 0 ..$ len ) . map ( | _ | read_value ! ( $ iter , $ t ) ) . collect ::< Vec < _ >> ( ) } ; ( $ iter : expr , { chars : $ base : expr } ) => { read_value ! ( $ iter , String ) . chars ( ) . map ( | c | ( c as u8 - $ base as u8 ) as usize ) . collect ::< Vec < usize >> ( ) } ; ( $ iter : expr , { char : $ base : expr } ) => { read_value ! ( $ iter , { chars : $ base } ) [ 0 ] } ; ( $ iter : expr , chars ) => { read_value ! ( $ iter , String ) . chars ( ) . collect ::< Vec < char >> ( ) } ; ( $ iter : expr , char ) => { read_value ! ( $ iter , chars ) [ 0 ] } ; ( $ iter : expr , usize1 ) => { read_value ! ( $ iter , usize ) - 1 } ; ( $ iter : expr , $ t : ty ) => { $ iter . next ( ) . unwrap ( ) . parse ::<$ t > ( ) . unwrap ( ) } ; }
pub mod at {
    // use std;
    #[inline]
    fn rmb(k: usize) -> usize {
        (k as isize & -(k as isize)) as usize
    }
    pub trait Monoid {
        type T: Clone + PartialEq;
        fn mempty(&self) -> Self::T;
        fn mappend(&self, x: &Self::T, y: &Self::T) -> Self::T;
    }
    pub struct BinaryIndexedTree<M: Monoid> {
        bit: Vec<M::T>,
        m: M,
    }
    impl<M: Monoid> BinaryIndexedTree<M> {
        pub fn new(n: usize, m: M) -> BinaryIndexedTree<M> {
            let bit = vec![m.mempty(); n + 1];
            BinaryIndexedTree { bit: bit, m: m }
        }
        #[doc = " 1-indexed"]
        pub fn query(&self, k: usize) -> M::T {
            let mut res = self.m.mempty();
            let mut k = k;
            while k > 0 {
                res = self.m.mappend(&res, &self.bit[k]);
                k -= rmb(k);
            }
            res
        }
        #[doc = " 1-indexed"]
        pub fn update(&mut self, k: usize, x: M::T) {
            let mut k = k;
            while k < self.bit.len() {
                self.bit[k] = self.m.mappend(&self.bit[k], &x);
                k += rmb(k);
            }
        }
    }
    pub trait Group: Monoid {
        fn invert(&self, x: &Self::T) -> Self::T;
    }
    impl<G: Group> BinaryIndexedTree<G> {
        #[doc = " 0-indexed [l, r)"]
        pub fn query_section(&self, l: usize, r: usize) -> G::T {
            self.m
                .mappend(&self.m.invert(&self.query(l)), &self.query(r))
        }
        #[doc = " 1-indexed"]
        pub fn get_val(&self, k: usize) -> G::T {
            self.query_section(k - 1, k)
        }
        #[doc = " 1-indexed"]
        pub fn set_val(&mut self, k: usize, x: G::T) {
            let y = self.m.invert(&self.get_val(k));
            let z = self.m.mappend(&y, &x);
            self.update(k, z);
        }
    }
    pub struct AnyMonoid<T: Clone, F: Fn(&T, &T) -> T> {
        id: T,
        op: F,
    }
    impl<T: Clone, F: Fn(&T, &T) -> T> AnyMonoid<T, F> {
        pub fn new(id: T, op: F) -> AnyMonoid<T, F> {
            AnyMonoid { id: id, op: op }
        }
    }
    impl<T: Clone + PartialEq, F: Fn(&T, &T) -> T> Monoid for AnyMonoid<T, F> {
        type T = T;
        fn mempty(&self) -> T {
            self.id.clone()
        }
        fn mappend(&self, x: &T, y: &T) -> T {
            (self.op)(x, y)
        }
    }
    pub struct AnyGroup<T: Clone, F: Fn(&T, &T) -> T, G: Fn(&T) -> T> {
        id: T,
        op: F,
        inv: G,
    }
    impl<T: Clone, F: Fn(&T, &T) -> T, G: Fn(&T) -> T> AnyGroup<T, F, G> {
        pub fn new(id: T, op: F, inv: G) -> AnyGroup<T, F, G> {
            AnyGroup {
                id: id,
                op: op,
                inv: inv,
            }
        }
    }
    impl<T: Clone + PartialEq, F: Fn(&T, &T) -> T, G: Fn(&T) -> T> Monoid for AnyGroup<T, F, G> {
        type T = T;
        fn mempty(&self) -> T {
            self.id.clone()
        }
        fn mappend(&self, x: &T, y: &T) -> T {
            (self.op)(x, y)
        }
    }
    impl<T: Clone + PartialEq, F: Fn(&T, &T) -> T, G: Fn(&T) -> T> Group for AnyGroup<T, F, G> {
        fn invert(&self, x: &T) -> T {
            (self.inv)(x)
        }
    }
    pub trait Bisect: Copy {
        fn halve(self, other: Self) -> Self;
        fn section_end(self, other: Self) -> bool;
    }
    impl Bisect for usize {
        fn halve(self, other: Self) -> Self {
            if self > other {
                other + (self - other) / 2
            } else {
                self + (other - self) / 2
            }
        }
        fn section_end(self, other: Self) -> bool {
            (if self > other {
                self - other
            } else {
                other - self
            }) <= 1
        }
    }
    impl Bisect for i64 {
        fn halve(self, other: Self) -> Self {
            (self + other) / 2
        }
        fn section_end(self, other: Self) -> bool {
            (self - other).abs() <= 1
        }
    }
    impl Bisect for f64 {
        fn halve(self, other: Self) -> Self {
            (self + other) / 2.
        }
        fn section_end(self, other: Self) -> bool {
            (self - other).abs() <= 1e-8
        }
    }
    pub fn binary_search<T: Bisect, F: Fn(T) -> bool>(f: F, ok: T, err: T) -> T {
        let mut ok = ok;
        let mut err = err;
        while !ok.section_end(err) {
            let m = ok.halve(err);
            if f(m) {
                ok = m;
            } else {
                err = m;
            }
        }
        ok
    }
    pub fn lower_bound<T: Bisect + Ord>(v: &[T], x: T) -> usize {
        binary_search(|i| v[i as usize] >= x, v.len() as i64, -1) as usize
    }
    impl<M: Monoid> BinaryIndexedTree<M>
    where
        M::T: Ord,
    {
        #[doc = " 0-indexed"]
        pub fn lower_bound(&self, x: M::T) -> (usize, M::T) {
            let n = self.bit.len() - 1;
            let mut acc = self.m.mempty();
            let mut pos = 0;
            let mut k = 1 << format!("{:b}", n).len();
            while k > 0 {
                if k + pos <= n && self.m.mappend(&acc, &self.bit[k + pos]) < x {
                    pos += k;
                    acc = self.m.mappend(&acc, &self.bit[pos]);
                }
                k >>= 1;
            }
            (pos, acc)
        }
    }
}
use at::*;
use std::collections::BTreeSet;
fn main() {
    input! { iter = iter, q };
    let mut update_query = vec![];
    let mut minimum_query = vec![];
    for _ in 0..q {
        input_inner! { iter, x };
        if x == 1 {
            input_inner! { iter, a: i64, b: i64 };
            update_query.push((a, b));
        } else {
            minimum_query.push(update_query.len() - 1);
        }
    }
    let v = update_query
        .iter()
        .map(|&(a, _)| a)
        .collect::<BTreeSet<_>>()
        .into_iter()
        .collect::<Vec<_>>();
    let mut bitm = BinaryIndexedTree::new(v.len(), AnyGroup::new(0, |&x, &y| x + y, |&x| -x));
    let mut bitc = BinaryIndexedTree::new(v.len(), AnyGroup::new(0, |&x, &y| x + y, |&x| -x));
    let mut acc = 0;
    let mut j = 0;
    for (i, &(a, b)) in update_query.iter().enumerate() {
        let k = lower_bound(&v, a) + 1;
        bitm.update(k, a);
        bitc.update(k, 1);
        acc += b;
        while j < minimum_query.len() && i == minimum_query[j] {
            let (k, _sxx) = bitc.lower_bound(i as i64 / 2 + 1);
            let mut ans = bitm.query_section(k + 1, v.len()) - bitm.query_section(0, k + 1);
            ans += (i as i64 + 1 - 2 * bitc.query_section(k + 1, v.len())) * v[k] + acc;
            println!("{} {}", v[k], ans);
            j += 1;
        }
    }
}