Problem:
LCA: Lowest Common Ancestor

For a rooted tree, find the lowest common ancestor of two nodes u and v.

The given tree consists of n nodes and every node has a unique ID from 0 to n-1 where 0 is the root.

Input

n
k0 c1 c2 ... ck0
k1 c1 c2 ... ck1
:
kn-1 c1 c2 ... ckn-1
q
u1 v1
u2 v2
:
uq vq

The first line of the input includes an integer n, the number of nodes of the tree.

In the next n lines, the information of node i is given. ki is the number of children of node i, and c1, ... cki are node IDs of 1st, ... kth child of node i.

In the next line, the number of queryies q is given. In the next q lines, pairs of u and v are given as the queries.

Output

For each query, print the LCA of u and v in a line.

Constraints

1 ≤ n ≤ 100000

1 ≤ q ≤ 100000

Sample Input 1

8
3 1 2 3
2 4 5
0
0
0
2 6 7
0
0
4
4 6
4 7
4 3
5 2

Sample Output 1

1
1
0
0

Solution in Rust (judge verdict: Accepted)

#[doc = " https://github.com/hatoo/competitive-rust-snippets"]
#[allow(unused_imports)]
use std::cmp::{max, min, Ordering};
#[allow(unused_imports)]
use std::collections::{BTreeMap, BTreeSet, BinaryHeap, HashMap, HashSet, VecDeque};
#[allow(unused_imports)]
use std::io::{stdin, stdout, BufWriter, Write};
#[allow(unused_imports)]
use std::iter::FromIterator;
#[allow(unused_macros)]
macro_rules ! debug { ( $ ( $ a : expr ) ,* ) => { eprintln ! ( concat ! ( $ ( stringify ! ( $ a ) , " = {:?}, " ) ,* ) , $ ( $ a ) ,* ) ; } }
#[macro_export]
macro_rules ! input { ( source = $ s : expr , $ ( $ r : tt ) * ) => { let mut parser = Parser :: from_str ( $ s ) ; input_inner ! { parser , $ ( $ r ) * } } ; ( parser = $ parser : ident , $ ( $ r : tt ) * ) => { input_inner ! { $ parser , $ ( $ r ) * } } ; ( new_stdin_parser = $ parser : ident , $ ( $ r : tt ) * ) => { let stdin = std :: io :: stdin ( ) ; let reader = std :: io :: BufReader :: new ( stdin . lock ( ) ) ; let mut $ parser = Parser :: new ( reader ) ; input_inner ! { $ parser , $ ( $ r ) * } } ; ( $ ( $ r : tt ) * ) => { input ! { new_stdin_parser = parser , $ ( $ r ) * } } ; }
#[macro_export]
macro_rules ! input_inner { ( $ parser : ident ) => { } ; ( $ parser : ident , ) => { } ; ( $ parser : ident , $ var : ident : $ t : tt $ ( $ r : tt ) * ) => { let $ var = read_value ! ( $ parser , $ t ) ; input_inner ! { $ parser $ ( $ r ) * } } ; }
#[macro_export]
macro_rules ! read_value { ( $ parser : ident , ( $ ( $ t : tt ) ,* ) ) => { ( $ ( read_value ! ( $ parser , $ t ) ) ,* ) } ; ( $ parser : ident , [ $ t : tt ; $ len : expr ] ) => { ( 0 ..$ len ) . map ( | _ | read_value ! ( $ parser , $ t ) ) . collect ::< Vec < _ >> ( ) } ; ( $ parser : ident , chars ) => { read_value ! ( $ parser , String ) . chars ( ) . collect ::< Vec < char >> ( ) } ; ( $ parser : ident , usize1 ) => { read_value ! ( $ parser , usize ) - 1 } ; ( $ parser : ident , $ t : ty ) => { $ parser . next ::<$ t > ( ) . expect ( "Parse error" ) } ; }
use std::io;
use std::io::BufRead;
use std::str;
pub struct Parser<R> {
    reader: R,
    buf: Vec<u8>,
    pos: usize,
}
impl Parser<io::Empty> {
    pub fn from_str(s: &str) -> Parser<io::Empty> {
        Parser {
            reader: io::empty(),
            buf: s.as_bytes().to_vec(),
            pos: 0,
        }
    }
}
impl<R: BufRead> Parser<R> {
    pub fn new(reader: R) -> Parser<R> {
        Parser {
            reader: reader,
            buf: vec![],
            pos: 0,
        }
    }
    pub fn update_buf(&mut self) {
        self.buf.clear();
        self.pos = 0;
        loop {
            let (len, complete) = {
                let buf2 = self.reader.fill_buf().unwrap();
                self.buf.extend_from_slice(buf2);
                let len = buf2.len();
                if len == 0 {
                    break;
                }
                (len, buf2[len - 1] <= 0x20)
            };
            self.reader.consume(len);
            if complete {
                break;
            }
        }
    }
    pub fn next<T: str::FromStr>(&mut self) -> Result<T, T::Err> {
        loop {
            let mut begin = self.pos;
            while begin < self.buf.len() && (self.buf[begin] <= 0x20) {
                begin += 1;
            }
            let mut end = begin;
            while end < self.buf.len() && (self.buf[end] > 0x20) {
                end += 1;
            }
            if begin != self.buf.len() {
                self.pos = end;
                return str::from_utf8(&self.buf[begin..end]).unwrap().parse::<T>();
            } else {
                self.update_buf();
            }
        }
    }
}
#[allow(unused_macros)]
macro_rules ! debug { ( $ ( $ a : expr ) ,* ) => { eprintln ! ( concat ! ( $ ( stringify ! ( $ a ) , " = {:?}, " ) ,* ) , $ ( $ a ) ,* ) ; } }
#[doc = " https://github.com/hatoo/competitive-rust-snippets"]
const BIG_STACK_SIZE: bool = true;
#[allow(dead_code)]
fn main() {
    use std::thread;
    if BIG_STACK_SIZE {
        thread::Builder::new()
            .stack_size(32 * 1024 * 1024)
            .name("solve".into())
            .spawn(solve)
            .unwrap()
            .join()
            .unwrap();
    } else {
        solve();
    }
}
struct LCA <'a> {
    root: usize,
    tree: &'a [Vec<usize>],
    parent: Vec<Vec<Option<usize>>>,
    depth: Vec<u32>,
}

impl <'a> LCA<'a> {
    fn new(root: usize, tree: &'a [Vec<usize>]) -> Self {
        let n = tree.len();
        let mut log_n = (n as f64).log2().ceil() as usize;
        if log_n == 0 {
            log_n = 1;
        }
        assert!(log_n > 0);
        Self {
            root,
            tree,
            parent: vec![vec![None; n]; log_n],
            depth: vec![0; n],
        }
    }
    // store direct parent and depth
    fn dfs(&mut self, u: usize, parent: Option<usize>, depth: u32) {
        self.parent[0][u] = parent;
        self.depth[u] = depth;
        for i in 0 .. self.tree[u].len() {
            let v = self.tree[u][i];
            if Some(v) != parent {
                self.dfs(v, Some(u), depth+1);
            }
        }
    }
    fn build(&mut self) {
        let root = self.root;
        self.dfs(root, None, 0);

        let mut k = 0;
        while k+1 < self.parent.len() {
            for u in 0 .. self.tree.len() {
                if self.parent[k][u].is_some() {
                    self.parent[k+1][u] = self.parent[k][self.parent[k][u].unwrap()]
                } 
            }
            k += 1;
        }
    }
    fn lca(&self, u: usize, v: usize) -> usize {
        let (mut v0, mut v1) = if self.depth[u] <= self.depth[v] {
            (u, v)
        } else {
            (v, u)
        };
        assert!(self.depth[v1] >= self.depth[v0]);

        // move v1 up until depth of v0 and v1 gets equal.
        for k in 0 .. self.parent.len() {
            if (((self.depth[v1] - self.depth[v0]) >> k) & 1) > 0 {
                assert!(self.parent[k][v1].is_some());
                v1 = self.parent[k][v1].unwrap();
            }
        }
        assert!(self.depth[v1] >= self.depth[v0]);
        assert!(self.depth[v1] == self.depth[v0]);
        if (v0 == v1) {
            return v0;
        }
        for k in (0..self.parent.len()).rev() {
            // LCA's parent is LCA
            if self.parent[k][v0] != self.parent[k][v1] {
                assert!(self.parent[k][v0].is_some());
                assert!(self.parent[k][v1].is_some());
                v0 = self.parent[k][v0].unwrap();
                v1 = self.parent[k][v1].unwrap();
            }
        }
        return self.parent[0][v0].unwrap();
    }
}
fn solve() {
    input! {
        new_stdin_parser = parser,
        N: usize,
    }
    let mut tree = vec![vec![]; N];
    for i in 0..N {
        input! {
            parser = parser,
            k: usize,
        }
        input! {
            parser = parser,
            cs: [usize; k]
        }
        for c in cs {
            tree[i].push(c);
            tree[c].push(i);
        }
    }

    let mut lca = LCA::new(0, &tree);
    lca.build();

    input! {
        parser = parser,
        Q: usize,
        qs: [(usize, usize); Q]
    }
    for (u,v) in qs {
        let p = lca.lca(u, v);
        println!("{}", p);
    }
}