// https://contest.ucup.ac/contest/1903/problem/9696
use crate::algo_lib::collections::min_max::MinimMaxim;
use crate::algo_lib::collections::vec_ext::inc_dec::IncDec;
use crate::algo_lib::graph::edge_distances::BiEdgeAlgos;
use crate::algo_lib::graph::edges::edge_trait::EdgeTrait;
use crate::algo_lib::graph::Graph;
use crate::algo_lib::io::input::Input;
use crate::algo_lib::io::output::Output;
use crate::algo_lib::misc::recursive_function::{Callable2, RecursiveFunction2};
use crate::algo_lib::misc::test_type::TaskType;
use crate::algo_lib::misc::test_type::TestType;
type PreCalc = ();
fn solve(input: &mut Input, out: &mut Output, _test_case: usize, _data: &mut PreCalc) {
    let n = input.read_size();
    let a = input.read_long();
    let b = input.read_long();
    let edges = input.read_size_pair_vec(n - 1).dec();
    let graph = Graph::with_biedges(n, &edges);
    let diam = graph.diameter();
    if b > a * diam as i64 {
        out.print_line(a * (n - 1 - diam) as i64);
        return;
    }
    let mut dfs = RecursiveFunction2::new(|f, vert: usize, prev: usize| -> (i64, i64) {
        let mut calls = Vec::new();
        for e in &graph[vert] {
            if e.to() == prev {
                continue;
            }
            let call = f.call(e.to(), vert);
            calls.push(call);
        }
        calls.sort_unstable_by_key(|&(x, y)| x - y);
        let sum_y: i64 = calls.iter().map(|&(_, y)| y).sum();
        let mut y = sum_y;
        let mut cur_y = sum_y;
        for i in (2..=calls.len()).step_by(2) {
            cur_y -= calls[i - 2].1 + calls[i - 1].1;
            cur_y += calls[i - 2].0 + calls[i - 1].0 + b;
            y.minim(cur_y);
        }
        let mut x = -a + sum_y;
        if !calls.is_empty() {
            x += calls[0].0 - calls[0].1;
        }
        let mut cur_x = x;
        for i in (3..=calls.len()).step_by(2) {
            cur_x -= calls[i - 2].1 + calls[i - 1].1;
            cur_x += calls[i - 2].0 + calls[i - 1].0 + b;
            x.minim(cur_x);
        }
        (x, y)
    });
    let (_, ans) = dfs.call(0, n);
    out.print_line(ans + a * (n as i64 - 1) - b);
}
pub static TEST_TYPE: TestType = TestType::Single;
pub static TASK_TYPE: TaskType = TaskType::Classic;
pub(crate) fn run(mut input: Input, mut output: Output) -> bool {
    let mut pre_calc = ();
    match TEST_TYPE {
        TestType::Single => solve(&mut input, &mut output, 1, &mut pre_calc),
        TestType::MultiNumber => {
            let t = input.read();
            for i in 1..=t {
                solve(&mut input, &mut output, i, &mut pre_calc);
            }
        }
        TestType::MultiEof => {
            let mut i = 1;
            while input.peek().is_some() {
                solve(&mut input, &mut output, i, &mut pre_calc);
                i += 1;
            }
        }
    }
    output.flush();
    match TASK_TYPE {
        TaskType::Classic => input.is_empty(),
        TaskType::Interactive => true,
    }
}


fn main() {
    let input = crate::algo_lib::io::input::Input::stdin();
    let output = crate::algo_lib::io::output::Output::stdout();
    run(input, output);
}
pub mod algo_lib {
pub mod collections {
pub mod dsu {
use crate::algo_lib::collections::slice_ext::bounds::Bounds;
use crate::algo_lib::collections::slice_ext::indices::Indices;
use std::cell::Cell;
#[derive(Clone)]
pub struct DSU {
    id: Vec<Cell<i32>>,
    count: usize,
}
impl DSU {
    pub fn new(n: usize) -> Self {
        Self {
            id: vec![Cell::new(- 1); n],
            count: n,
        }
    }
    pub fn size(&self, i: usize) -> usize {
        (-self.id[self.find(i)].get()) as usize
    }
    #[allow(clippy::len_without_is_empty)]
    pub fn len(&self) -> usize {
        self.id.len()
    }
    pub fn iter(&self) -> impl Iterator<Item = usize> + '_ {
        self.id
            .iter()
            .enumerate()
            .filter_map(|(i, id)| if id.get() < 0 { Some(i) } else { None })
    }
    pub fn set_count(&self) -> usize {
        self.count
    }
    pub fn union(&mut self, mut a: usize, mut b: usize) -> bool {
        a = self.find(a);
        b = self.find(b);
        if a == b {
            false
        } else {
            self.id[a].set(self.id[a].get() + self.id[b].get());
            self.id[b].set(a as i32);
            self.count -= 1;
            true
        }
    }
    pub fn find(&self, i: usize) -> usize {
        if self.id[i].get() >= 0 {
            let res = self.find(self.id[i].get() as usize);
            self.id[i].set(res as i32);
            res
        } else {
            i
        }
    }
    pub fn clear(&mut self) {
        self.count = self.id.len();
        self.id.fill(Cell::new(-1));
    }
    pub fn parts(&self) -> Vec<Vec<usize>> {
        let roots: Vec<_> = self.iter().collect();
        let mut res = vec![Vec::new(); roots.len()];
        for i in self.id.indices() {
            res[roots.as_slice().bin_search(&self.find(i)).unwrap()].push(i);
        }
        res
    }
}
}
pub mod iter_ext {
pub mod iters {
use std::iter::{Chain, Enumerate, Filter, Map, Rev, Skip, StepBy, Sum, Take, Zip};
pub trait Iters: IntoIterator + Sized {
    fn iter_enumerate(self) -> Enumerate<Self::IntoIter> {
        self.into_iter().enumerate()
    }
    fn iter_rev(self) -> Rev<Self::IntoIter>
    where
        Self::IntoIter: DoubleEndedIterator,
    {
        self.into_iter().rev()
    }
    fn iter_skip(self, n: usize) -> Skip<Self::IntoIter> {
        self.into_iter().skip(n)
    }
    fn iter_take(self, n: usize) -> Take<Self::IntoIter> {
        self.into_iter().take(n)
    }
    fn iter_chain<V: IntoIterator<Item = Self::Item>>(
        self,
        chained: V,
    ) -> Chain<Self::IntoIter, V::IntoIter> {
        self.into_iter().chain(chained)
    }
    fn iter_zip<V: IntoIterator>(self, other: V) -> Zip<Self::IntoIter, V::IntoIter> {
        self.into_iter().zip(other)
    }
    fn iter_max(self) -> Self::Item
    where
        Self::Item: Ord,
    {
        self.into_iter().max().unwrap()
    }
    fn iter_max_by_key<B, F>(self, f: F) -> Self::Item
    where
        F: FnMut(&Self::Item) -> B,
        B: Ord,
    {
        self.into_iter().max_by_key(f).unwrap()
    }
    fn iter_min(self) -> Self::Item
    where
        Self::Item: Ord,
    {
        self.into_iter().min().unwrap()
    }
    fn iter_min_by_key<B, F>(self, f: F) -> Self::Item
    where
        F: FnMut(&Self::Item) -> B,
        B: Ord,
    {
        self.into_iter().min_by_key(f).unwrap()
    }
    fn iter_sum(self) -> Self::Item
    where
        Self::Item: Sum<Self::Item>,
    {
        Sum::sum(self.into_iter())
    }
    fn iter_map<F, T>(self, f: F) -> Map<Self::IntoIter, F>
    where
        F: FnMut(Self::Item) -> T,
    {
        self.into_iter().map(f)
    }
    fn iter_all(self, f: impl FnMut(Self::Item) -> bool) -> bool {
        self.into_iter().all(f)
    }
    fn iter_any(self, f: impl FnMut(Self::Item) -> bool) -> bool {
        self.into_iter().any(f)
    }
    fn iter_step_by(self, step: usize) -> StepBy<Self::IntoIter> {
        self.into_iter().step_by(step)
    }
    fn iter_filter<F: FnMut(&Self::Item) -> bool>(
        self,
        f: F,
    ) -> Filter<Self::IntoIter, F> {
        self.into_iter().filter(f)
    }
    fn iter_fold<Acc, F>(self, init: Acc, f: F) -> Acc
    where
        F: FnMut(Acc, Self::Item) -> Acc,
    {
        self.into_iter().fold(init, f)
    }
    fn iter_reduce<F>(self, f: F) -> Option<Self::Item>
    where
        F: FnMut(Self::Item, Self::Item) -> Self::Item,
    {
        self.into_iter().reduce(f)
    }
    fn iter_position<P>(self, predicate: P) -> Option<usize>
    where
        P: FnMut(Self::Item) -> bool,
    {
        self.into_iter().position(predicate)
    }
    fn iter_find(self, val: Self::Item) -> Option<usize>
    where
        Self::Item: PartialEq,
    {
        self.into_iter().position(|x| x == val)
    }
    fn iter_count(self, val: Self::Item) -> usize
    where
        Self::Item: PartialEq,
    {
        self.into_iter().filter(|x| *x == val).count()
    }
}
impl<U> Iters for U
where
    U: IntoIterator,
{}
}
pub mod min_max {
use crate::algo_lib::collections::min_max::MinimMaxim;
pub trait IterMinMaxPos<'a, T: Ord + 'a>: 'a
where
    &'a Self: IntoIterator<Item = T>,
{
    fn max_position(&'a self) -> usize {
        let mut res = None;
        let mut val = None;
        for (i, cur) in self.into_iter().enumerate() {
            if val.maxim(cur) {
                res = Some(i);
            }
        }
        res.unwrap()
    }
    fn min_position(&'a self) -> usize {
        let mut res = None;
        let mut val = None;
        for (i, cur) in self.into_iter().enumerate() {
            if val.minim(cur) {
                res = Some(i);
            }
        }
        res.unwrap()
    }
}
impl<'a, T: Ord + 'a, I: ?Sized + 'a> IterMinMaxPos<'a, T> for I
where
    &'a I: IntoIterator<Item = T>,
{}
}
}
pub mod min_max {
pub trait MinimMaxim<Rhs = Self>: PartialOrd + Sized {
    fn minim(&mut self, other: Rhs) -> bool;
    fn maxim(&mut self, other: Rhs) -> bool;
}
impl<T: PartialOrd> MinimMaxim for T {
    fn minim(&mut self, other: Self) -> bool {
        if other < *self {
            *self = other;
            true
        } else {
            false
        }
    }
    fn maxim(&mut self, other: Self) -> bool {
        if other > *self {
            *self = other;
            true
        } else {
            false
        }
    }
}
impl<T: PartialOrd> MinimMaxim<T> for Option<T> {
    fn minim(&mut self, other: T) -> bool {
        match self {
            None => {
                *self = Some(other);
                true
            }
            Some(v) => v.minim(other),
        }
    }
    fn maxim(&mut self, other: T) -> bool {
        match self {
            None => {
                *self = Some(other);
                true
            }
            Some(v) => v.maxim(other),
        }
    }
}
}
pub mod slice_ext {
pub mod bounds {
use std::ops::{Bound, RangeBounds};
pub trait Bounds<T: PartialOrd> {
    fn lower_bound(&self, el: &T) -> usize;
    fn upper_bound(&self, el: &T) -> usize;
    fn bin_search(&self, el: &T) -> Option<usize>;
    fn more(&self, el: &T) -> usize;
    fn more_or_eq(&self, el: &T) -> usize;
    fn less(&self, el: &T) -> usize {
        self.lower_bound(el)
    }
    fn less_or_eq(&self, el: &T) -> usize {
        self.upper_bound(el)
    }
    fn inside<'a>(&self, bounds: impl RangeBounds<&'a T>) -> usize
    where
        T: 'a;
}
impl<T: PartialOrd> Bounds<T> for [T] {
    fn lower_bound(&self, el: &T) -> usize {
        let mut left = 0;
        let mut right = self.len();
        while left < right {
            let mid = left + ((right - left) >> 1);
            if &self[mid] < el {
                left = mid + 1;
            } else {
                right = mid;
            }
        }
        left
    }
    fn upper_bound(&self, el: &T) -> usize {
        let mut left = 0;
        let mut right = self.len();
        while left < right {
            let mid = left + ((right - left) >> 1);
            if &self[mid] <= el {
                left = mid + 1;
            } else {
                right = mid;
            }
        }
        left
    }
    fn bin_search(&self, el: &T) -> Option<usize> {
        let at = self.lower_bound(el);
        if at == self.len() || &self[at] != el { None } else { Some(at) }
    }
    fn more(&self, el: &T) -> usize {
        self.len() - self.upper_bound(el)
    }
    fn more_or_eq(&self, el: &T) -> usize {
        self.len() - self.lower_bound(el)
    }
    fn inside<'a>(&self, bounds: impl RangeBounds<&'a T>) -> usize
    where
        T: 'a,
    {
        let to = match bounds.end_bound() {
            Bound::Included(el) => self.less_or_eq(el),
            Bound::Excluded(el) => self.less(el),
            Bound::Unbounded => self.len(),
        };
        let from = match bounds.start_bound() {
            Bound::Included(el) => self.less(el),
            Bound::Excluded(el) => self.less_or_eq(el),
            Bound::Unbounded => 0,
        };
        to - from
    }
}
}
pub mod indices {
use std::ops::Range;
pub trait Indices {
    fn indices(&self) -> Range<usize>;
}
impl<T> Indices for [T] {
    fn indices(&self) -> Range<usize> {
        0..self.len()
    }
}
}
}
pub mod vec_ext {
pub mod inc_dec {
use crate::algo_lib::numbers::num_traits::algebra::{AdditionMonoidWithSub, One};
pub trait IncDec {
    #[must_use]
    fn inc(self) -> Self;
    #[must_use]
    fn dec(self) -> Self;
}
impl<T: AdditionMonoidWithSub + One> IncDec for T {
    fn inc(self) -> Self {
        self + T::one()
    }
    fn dec(self) -> Self {
        self - T::one()
    }
}
impl<T: AdditionMonoidWithSub + One> IncDec for Vec<T> {
    fn inc(mut self) -> Self {
        self.iter_mut().for_each(|i| *i += T::one());
        self
    }
    fn dec(mut self) -> Self {
        self.iter_mut().for_each(|i| *i -= T::one());
        self
    }
}
impl<T: AdditionMonoidWithSub + One> IncDec for Vec<Vec<T>> {
    fn inc(mut self) -> Self {
        self.iter_mut().for_each(|v| v.iter_mut().for_each(|i| *i += T::one()));
        self
    }
    fn dec(mut self) -> Self {
        self.iter_mut().for_each(|v| v.iter_mut().for_each(|i| *i -= T::one()));
        self
    }
}
impl<T: AdditionMonoidWithSub + One, U: AdditionMonoidWithSub + One> IncDec
for Vec<(T, U)> {
    fn inc(mut self) -> Self {
        self.iter_mut()
            .for_each(|(i, j)| {
                *i += T::one();
                *j += U::one();
            });
        self
    }
    fn dec(mut self) -> Self {
        self.iter_mut()
            .for_each(|(i, j)| {
                *i -= T::one();
                *j -= U::one();
            });
        self
    }
}
impl<T: AdditionMonoidWithSub + One, U: AdditionMonoidWithSub + One, V> IncDec
for Vec<(T, U, V)> {
    fn inc(mut self) -> Self {
        self.iter_mut()
            .for_each(|(i, j, _)| {
                *i += T::one();
                *j += U::one();
            });
        self
    }
    fn dec(mut self) -> Self {
        self.iter_mut()
            .for_each(|(i, j, _)| {
                *i -= T::one();
                *j -= U::one();
            });
        self
    }
}
impl<T: AdditionMonoidWithSub + One, U: AdditionMonoidWithSub + One, V, W> IncDec
for Vec<(T, U, V, W)> {
    fn inc(mut self) -> Self {
        self.iter_mut()
            .for_each(|(i, j, ..)| {
                *i += T::one();
                *j += U::one();
            });
        self
    }
    fn dec(mut self) -> Self {
        self.iter_mut()
            .for_each(|(i, j, ..)| {
                *i -= T::one();
                *j -= U::one();
            });
        self
    }
}
impl<T: AdditionMonoidWithSub + One, U: AdditionMonoidWithSub + One, V, W, X> IncDec
for Vec<(T, U, V, W, X)> {
    fn inc(mut self) -> Self {
        self.iter_mut()
            .for_each(|(i, j, ..)| {
                *i += T::one();
                *j += U::one();
            });
        self
    }
    fn dec(mut self) -> Self {
        self.iter_mut()
            .for_each(|(i, j, ..)| {
                *i -= T::one();
                *j -= U::one();
            });
        self
    }
}
impl<T: AdditionMonoidWithSub + One, U: AdditionMonoidWithSub + One> IncDec for (T, U) {
    fn inc(mut self) -> Self {
        self.0 += T::one();
        self.1 += U::one();
        self
    }
    fn dec(mut self) -> Self {
        self.0 -= T::one();
        self.1 -= U::one();
        self
    }
}
}
}
}
pub mod graph {
use crate::algo_lib::collections::dsu::DSU;
use crate::algo_lib::graph::edges::bi_edge::BiEdge;
use crate::algo_lib::graph::edges::edge::Edge;
use crate::algo_lib::graph::edges::edge_trait::{BidirectionalEdgeTrait, EdgeTrait};
use std::ops::{Index, IndexMut};




















#[derive(Clone)]
pub struct Graph<E: EdgeTrait> {
    edges: Vec<Vec<E>>,
    edge_count: usize,
}
impl<E: EdgeTrait> Graph<E> {
    pub fn new(vertex_count: usize) -> Self {
        Self {
            edges: vec![Vec::new(); vertex_count],
            edge_count: 0,
        }
    }
    pub fn add_edge(&mut self, (from, mut edge): (usize, E)) -> usize {
        let to = edge.to();
        assert!(to < self.vertex_count());
        let direct_id = self.edges[from].len();
        edge.set_id(self.edge_count);
        self.edges[from].push(edge);
        if E::REVERSABLE {
            let rev_id = self.edges[to].len();
            self.edges[from][direct_id].set_reverse_id(rev_id);
            let mut rev_edge = self.edges[from][direct_id].reverse_edge(from);
            rev_edge.set_id(self.edge_count);
            rev_edge.set_reverse_id(direct_id);
            self.edges[to].push(rev_edge);
        }
        self.edge_count += 1;
        direct_id
    }
    pub fn add_vertices(&mut self, cnt: usize) {
        self.edges.resize(self.edges.len() + cnt, Vec::new());
    }
    pub fn clear(&mut self) {
        self.edge_count = 0;
        for ve in self.edges.iter_mut() {
            ve.clear();
        }
    }
    pub fn vertex_count(&self) -> usize {
        self.edges.len()
    }
    pub fn edge_count(&self) -> usize {
        self.edge_count
    }
    pub fn degrees(&self) -> Vec<usize> {
        self.edges.iter().map(|v| v.len()).collect()
    }
}
impl<E: BidirectionalEdgeTrait> Graph<E> {
    pub fn is_tree(&self) -> bool {
        if self.edge_count + 1 != self.vertex_count() {
            false
        } else {
            self.is_connected()
        }
    }
    pub fn is_forest(&self) -> bool {
        let mut dsu = DSU::new(self.vertex_count());
        for i in 0..self.vertex_count() {
            for e in self[i].iter() {
                if i <= e.to() && !dsu.union(i, e.to()) {
                    return false;
                }
            }
        }
        true
    }
    pub fn is_connected(&self) -> bool {
        let mut dsu = DSU::new(self.vertex_count());
        for i in 0..self.vertex_count() {
            for e in self[i].iter() {
                dsu.union(i, e.to());
            }
        }
        dsu.set_count() == 1
    }
}
impl<E: EdgeTrait> Index<usize> for Graph<E> {
    type Output = [E];
    fn index(&self, index: usize) -> &Self::Output {
        &self.edges[index]
    }
}
impl<E: EdgeTrait> IndexMut<usize> for Graph<E> {
    fn index_mut(&mut self, index: usize) -> &mut Self::Output {
        &mut self.edges[index]
    }
}
impl Graph<Edge<()>> {
    pub fn with_edges(n: usize, edges: &[(usize, usize)]) -> Self {
        let mut graph = Self::new(n);
        for &(from, to) in edges {
            graph.add_edge(Edge::new(from, to));
        }
        graph
    }
}
impl<P: Clone> Graph<Edge<P>> {
    pub fn with_edges_with_payload(n: usize, edges: &[(usize, usize, P)]) -> Self {
        let mut graph = Self::new(n);
        for (from, to, p) in edges.iter() {
            graph.add_edge(Edge::with_payload(*from, *to, p.clone()));
        }
        graph
    }
}
impl Graph<BiEdge<()>> {
    pub fn with_biedges(n: usize, edges: &[(usize, usize)]) -> Self {
        let mut graph = Self::new(n);
        for &(from, to) in edges {
            graph.add_edge(BiEdge::new(from, to));
        }
        graph
    }
}
impl<P: Clone> Graph<BiEdge<P>> {
    pub fn with_biedges_with_payload(n: usize, edges: &[(usize, usize, P)]) -> Self {
        let mut graph = Self::new(n);
        for (from, to, p) in edges.iter() {
            graph.add_edge(BiEdge::with_payload(*from, *to, p.clone()));
        }
        graph
    }
}
pub mod edge_distances {
use crate::algo_lib::collections::iter_ext::iters::Iters;
use crate::algo_lib::collections::iter_ext::min_max::IterMinMaxPos;
use crate::algo_lib::graph::edges::edge_trait::{BidirectionalEdgeTrait, EdgeTrait};
use crate::algo_lib::graph::Graph;
use std::collections::VecDeque;
pub trait EdgeAlgos {
    fn edge_distances(&self, source: usize) -> Vec<u32>;
}
pub trait BiEdgeAlgos: EdgeAlgos {
    fn centers(&self) -> Vec<usize>;
    fn diameter(&self) -> usize;
}
impl<E: EdgeTrait> EdgeAlgos for Graph<E> {
    fn edge_distances(&self, source: usize) -> Vec<u32> {
        let mut dist = vec![u32::MAX; self.vertex_count()];
        dist[source] = 0;
        let mut q = VecDeque::new();
        q.push_back(source);
        while !q.is_empty() {
            let cur = q.pop_front().unwrap();
            for e in self[cur].iter() {
                let next = e.to();
                if dist[next] == u32::MAX {
                    dist[next] = dist[cur] + 1;
                    q.push_back(next);
                }
            }
        }
        dist
    }
}
impl<E: BidirectionalEdgeTrait> BiEdgeAlgos for Graph<E> {
    fn centers(&self) -> Vec<usize> {
        debug_assert!(self.is_tree());
        if self.vertex_count() == 0 {
            return Vec::new();
        }
        let d0 = self.edge_distances(0);
        let first = d0.max_position();
        let d1 = self.edge_distances(first);
        let second = d1.max_position();
        let d2 = self.edge_distances(second);
        let mut res = Vec::new();
        let r1 = d1[second] / 2;
        let r2 = (d1[second] + 1) / 2;
        for (i, (d1, d2)) in d1.iter().zip(d2.iter()).enumerate() {
            if *d1 == r1 && *d2 == r2 || *d1 == r2 && *d2 == r1 {
                res.push(i);
            }
        }
        res
    }
    fn diameter(&self) -> usize {
        debug_assert!(self.is_tree());
        let d0 = self.edge_distances(0);
        let first = d0.max_position();
        let d1 = self.edge_distances(first);
        d1.iter_max() as usize
    }
}
}
pub mod edges {
pub mod bi_edge {
use crate::algo_lib::graph::edges::bi_edge_trait::BiEdgeTrait;
use crate::algo_lib::graph::edges::edge_id::{EdgeId, NoId, WithId};
use crate::algo_lib::graph::edges::edge_trait::{BidirectionalEdgeTrait, EdgeTrait};
#[derive(Clone)]
pub struct BiEdgeRaw<Id: EdgeId, P> {
    to: u32,
    id: Id,
    payload: P,
}
impl<Id: EdgeId> BiEdgeRaw<Id, ()> {
    pub fn new(from: usize, to: usize) -> (usize, Self) {
        (
            from,
            Self {
                to: to as u32,
                id: Id::new(),
                payload: (),
            },
        )
    }
}
impl<Id: EdgeId, P> BiEdgeRaw<Id, P> {
    pub fn with_payload(from: usize, to: usize, payload: P) -> (usize, Self) {
        (from, Self::with_payload_impl(to, payload))
    }
    fn with_payload_impl(to: usize, payload: P) -> BiEdgeRaw<Id, P> {
        Self {
            to: to as u32,
            id: Id::new(),
            payload,
        }
    }
}
impl<Id: EdgeId, P: Clone> BidirectionalEdgeTrait for BiEdgeRaw<Id, P> {}
impl<Id: EdgeId, P: Clone> EdgeTrait for BiEdgeRaw<Id, P> {
    type Payload = P;
    const REVERSABLE: bool = true;
    fn to(&self) -> usize {
        self.to as usize
    }
    fn id(&self) -> usize {
        self.id.id()
    }
    fn set_id(&mut self, id: usize) {
        self.id.set_id(id);
    }
    fn reverse_id(&self) -> usize {
        panic!("no reverse id")
    }
    fn set_reverse_id(&mut self, _: usize) {}
    fn reverse_edge(&self, from: usize) -> Self {
        Self::with_payload_impl(from, self.payload.clone())
    }
    fn payload(&self) -> &P {
        &self.payload
    }
}
impl<Id: EdgeId, P: Clone> BiEdgeTrait for BiEdgeRaw<Id, P> {}
pub type BiEdge<P> = BiEdgeRaw<NoId, P>;
pub type BiEdgeWithId<P> = BiEdgeRaw<WithId, P>;
}
pub mod bi_edge_trait {
use crate::algo_lib::graph::edges::edge_trait::EdgeTrait;
pub trait BiEdgeTrait: EdgeTrait {}
}
pub mod edge {
use crate::algo_lib::graph::edges::edge_id::{EdgeId, NoId, WithId};
use crate::algo_lib::graph::edges::edge_trait::EdgeTrait;
#[derive(Clone)]
pub struct EdgeRaw<Id: EdgeId, P> {
    to: u32,
    id: Id,
    payload: P,
}
impl<Id: EdgeId> EdgeRaw<Id, ()> {
    pub fn new(from: usize, to: usize) -> (usize, Self) {
        (
            from,
            Self {
                to: to as u32,
                id: Id::new(),
                payload: (),
            },
        )
    }
}
impl<Id: EdgeId, P> EdgeRaw<Id, P> {
    pub fn with_payload(from: usize, to: usize, payload: P) -> (usize, Self) {
        (from, Self::with_payload_impl(to, payload))
    }
    fn with_payload_impl(to: usize, payload: P) -> Self {
        Self {
            to: to as u32,
            id: Id::new(),
            payload,
        }
    }
}
impl<Id: EdgeId, P: Clone> EdgeTrait for EdgeRaw<Id, P> {
    type Payload = P;
    const REVERSABLE: bool = false;
    fn to(&self) -> usize {
        self.to as usize
    }
    fn id(&self) -> usize {
        self.id.id()
    }
    fn set_id(&mut self, id: usize) {
        self.id.set_id(id);
    }
    fn reverse_id(&self) -> usize {
        panic!("no reverse")
    }
    fn set_reverse_id(&mut self, _: usize) {
        panic!("no reverse")
    }
    fn reverse_edge(&self, _: usize) -> Self {
        panic!("no reverse")
    }
    fn payload(&self) -> &P {
        &self.payload
    }
}
pub type Edge<P> = EdgeRaw<NoId, P>;
pub type EdgeWithId<P> = EdgeRaw<WithId, P>;
}
pub mod edge_id {
pub trait EdgeId: Clone {
    fn new() -> Self;
    fn id(&self) -> usize;
    fn set_id(&mut self, id: usize);
}
#[derive(Clone)]
pub struct WithId {
    id: u32,
}
impl EdgeId for WithId {
    fn new() -> Self {
        Self { id: 0 }
    }
    fn id(&self) -> usize {
        self.id as usize
    }
    fn set_id(&mut self, id: usize) {
        self.id = id as u32;
    }
}
#[derive(Clone)]
pub struct NoId {}
impl EdgeId for NoId {
    fn new() -> Self {
        Self {}
    }
    fn id(&self) -> usize {
        panic!("Id called on no id")
    }
    fn set_id(&mut self, _: usize) {}
}
}
pub mod edge_trait {
pub trait EdgeTrait: Clone {
    type Payload;
    const REVERSABLE: bool;
    fn to(&self) -> usize;
    fn id(&self) -> usize;
    fn set_id(&mut self, id: usize);
    fn reverse_id(&self) -> usize;
    fn set_reverse_id(&mut self, reverse_id: usize);
    #[must_use]
    fn reverse_edge(&self, from: usize) -> Self;
    fn payload(&self) -> &Self::Payload;
}
pub trait BidirectionalEdgeTrait: EdgeTrait {}
}
}
}
pub mod io {
pub mod input {
use std::fs::File;
use std::io::{Read, Stdin};
use std::mem::MaybeUninit;
enum InputSource {
    Stdin(Stdin),
    File(File),
    Slice,
    Delegate(Box<dyn Read + Send>),
}
pub struct Input {
    input: InputSource,
    buf: Vec<u8>,
    at: usize,
    buf_read: usize,
    eol: bool,
}
macro_rules! read_impl {
    ($t:ty, $read_name:ident, $read_vec_name:ident) => {
        pub fn $read_name (& mut self) -> $t { self.read() } pub fn $read_vec_name (& mut
        self, len : usize) -> Vec <$t > { self.read_vec(len) }
    };
    ($t:ty, $read_name:ident, $read_vec_name:ident, $read_pair_vec_name:ident) => {
        read_impl!($t, $read_name, $read_vec_name); pub fn $read_pair_vec_name (& mut
        self, len : usize) -> Vec < ($t, $t) > { self.read_vec(len) }
    };
}
impl Input {
    const DEFAULT_BUF_SIZE: usize = 4096;
    pub fn slice(input: &[u8]) -> Self {
        Self {
            input: InputSource::Slice,
            buf: input.to_vec(),
            at: 0,
            buf_read: input.len(),
            eol: true,
        }
    }
    pub fn stdin() -> Self {
        Self {
            input: InputSource::Stdin(std::io::stdin()),
            buf: vec![0; Self::DEFAULT_BUF_SIZE],
            at: 0,
            buf_read: 0,
            eol: true,
        }
    }
    pub fn file(file: File) -> Self {
        Self {
            input: InputSource::File(file),
            buf: vec![0; Self::DEFAULT_BUF_SIZE],
            at: 0,
            buf_read: 0,
            eol: true,
        }
    }
    pub fn delegate(reader: impl Read + Send + 'static) -> Self {
        Self {
            input: InputSource::Delegate(Box::new(reader)),
            buf: vec![0; Self::DEFAULT_BUF_SIZE],
            at: 0,
            buf_read: 0,
            eol: true,
        }
    }
    pub fn get(&mut self) -> Option<u8> {
        if self.refill_buffer() {
            let res = self.buf[self.at];
            self.at += 1;
            if res == b'\r' {
                self.eol = true;
                if self.refill_buffer() && self.buf[self.at] == b'\n' {
                    self.at += 1;
                }
                return Some(b'\n');
            }
            self.eol = res == b'\n';
            Some(res)
        } else {
            None
        }
    }
    pub fn peek(&mut self) -> Option<u8> {
        if self.refill_buffer() {
            let res = self.buf[self.at];
            Some(if res == b'\r' { b'\n' } else { res })
        } else {
            None
        }
    }
    pub fn skip_whitespace(&mut self) {
        while let Some(b) = self.peek() {
            if !b.is_ascii_whitespace() {
                return;
            }
            self.get();
        }
    }
    pub fn next_token(&mut self) -> Option<Vec<u8>> {
        self.skip_whitespace();
        let mut res = Vec::new();
        while let Some(c) = self.get() {
            if c.is_ascii_whitespace() {
                break;
            }
            res.push(c);
        }
        if res.is_empty() { None } else { Some(res) }
    }
    pub fn is_exhausted(&mut self) -> bool {
        self.peek().is_none()
    }
    pub fn is_empty(&mut self) -> bool {
        self.skip_whitespace();
        self.is_exhausted()
    }
    pub fn read<T: Readable>(&mut self) -> T {
        T::read(self)
    }
    pub fn read_vec<T: Readable>(&mut self, size: usize) -> Vec<T> {
        let mut res = Vec::with_capacity(size);
        for _ in 0..size {
            res.push(self.read());
        }
        res
    }
    pub fn read_char(&mut self) -> u8 {
        self.skip_whitespace();
        self.get().unwrap()
    }
    read_impl!(u32, read_unsigned, read_unsigned_vec);
    read_impl!(u64, read_u64, read_u64_vec);
    read_impl!(usize, read_size, read_size_vec, read_size_pair_vec);
    read_impl!(i32, read_int, read_int_vec, read_int_pair_vec);
    read_impl!(i64, read_long, read_long_vec, read_long_pair_vec);
    read_impl!(i128, read_i128, read_i128_vec);
    fn refill_buffer(&mut self) -> bool {
        if self.at == self.buf_read {
            self.at = 0;
            self.buf_read = match &mut self.input {
                InputSource::Stdin(stdin) => stdin.read(&mut self.buf).unwrap(),
                InputSource::File(file) => file.read(&mut self.buf).unwrap(),
                InputSource::Delegate(reader) => reader.read(&mut self.buf).unwrap(),
                InputSource::Slice => 0,
            };
            self.buf_read != 0
        } else {
            true
        }
    }
    pub fn is_eol(&self) -> bool {
        self.eol
    }
}
pub trait Readable {
    fn read(input: &mut Input) -> Self;
}
impl Readable for u8 {
    fn read(input: &mut Input) -> Self {
        input.read_char()
    }
}
impl<T: Readable> Readable for Vec<T> {
    fn read(input: &mut Input) -> Self {
        let size = input.read();
        input.read_vec(size)
    }
}
impl<T: Readable, const SIZE: usize> Readable for [T; SIZE] {
    fn read(input: &mut Input) -> Self {
        unsafe {
            let mut res = MaybeUninit::<[T; SIZE]>::uninit();
            for i in 0..SIZE {
                let ptr: *mut T = (*res.as_mut_ptr()).as_mut_ptr();
                ptr.add(i).write(input.read::<T>());
            }
            res.assume_init()
        }
    }
}
macro_rules! read_integer {
    ($($t:ident)+) => {
        $(impl Readable for $t { fn read(input : & mut Input) -> Self { input
        .skip_whitespace(); let mut c = input.get().unwrap(); let sgn = match c { b'-' =>
        { c = input.get().unwrap(); true } b'+' => { c = input.get().unwrap(); false } _
        => false, }; let mut res = 0; loop { assert!(c.is_ascii_digit()); res *= 10; let
        d = (c - b'0') as $t; if sgn { res -= d; } else { res += d; } match input.get() {
        None => break, Some(ch) => { if ch.is_ascii_whitespace() { break; } else { c =
        ch; } } } } res } })+
    };
}
read_integer!(i8 i16 i32 i64 i128 isize u16 u32 u64 u128 usize);
macro_rules! tuple_readable {
    ($($name:ident)+) => {
        impl <$($name : Readable),+> Readable for ($($name,)+) { fn read(input : & mut
        Input) -> Self { ($($name ::read(input),)+) } }
    };
}
tuple_readable! {
    T
}
tuple_readable! {
    T U
}
tuple_readable! {
    T U V
}
tuple_readable! {
    T U V X
}
tuple_readable! {
    T U V X Y
}
tuple_readable! {
    T U V X Y Z
}
tuple_readable! {
    T U V X Y Z A
}
tuple_readable! {
    T U V X Y Z A B
}
tuple_readable! {
    T U V X Y Z A B C
}
tuple_readable! {
    T U V X Y Z A B C D
}
tuple_readable! {
    T U V X Y Z A B C D E
}
tuple_readable! {
    T U V X Y Z A B C D E F
}
}
pub mod output {
use std::cmp::Reverse;
use std::fs::File;
use std::io::{Stdout, Write};
#[derive(Copy, Clone)]
pub enum BoolOutput {
    YesNo,
    YesNoCaps,
    PossibleImpossible,
    Custom(&'static str, &'static str),
}
impl BoolOutput {
    pub fn output(&self, output: &mut Output, val: bool) {
        (if val { self.yes() } else { self.no() }).write(output);
    }
    fn yes(&self) -> &str {
        match self {
            BoolOutput::YesNo => "Yes",
            BoolOutput::YesNoCaps => "YES",
            BoolOutput::PossibleImpossible => "Possible",
            BoolOutput::Custom(yes, _) => yes,
        }
    }
    fn no(&self) -> &str {
        match self {
            BoolOutput::YesNo => "No",
            BoolOutput::YesNoCaps => "NO",
            BoolOutput::PossibleImpossible => "Impossible",
            BoolOutput::Custom(_, no) => no,
        }
    }
}
enum OutputDest<'s> {
    Stdout(Stdout),
    File(File),
    Buf(&'s mut Vec<u8>),
    Delegate(Box<dyn Write + 's>),
}
pub struct Output<'s> {
    output: OutputDest<'s>,
    buf: Vec<u8>,
    at: usize,
    bool_output: BoolOutput,
    precision: Option<usize>,
    separator: u8,
}
impl<'s> Output<'s> {
    pub fn buf(buf: &'s mut Vec<u8>) -> Self {
        Self::new(OutputDest::Buf(buf))
    }
    pub fn delegate(delegate: impl Write + 'static) -> Self {
        Self::new(OutputDest::Delegate(Box::new(delegate)))
    }
    fn new(output: OutputDest<'s>) -> Self {
        Self {
            output,
            buf: vec![0; Self::DEFAULT_BUF_SIZE],
            at: 0,
            bool_output: BoolOutput::YesNoCaps,
            precision: None,
            separator: b' ',
        }
    }
}
impl Output<'static> {
    pub fn stdout() -> Self {
        Self::new(OutputDest::Stdout(std::io::stdout()))
    }
    pub fn file(file: File) -> Self {
        Self::new(OutputDest::File(file))
    }
}
impl Output<'_> {
    const DEFAULT_BUF_SIZE: usize = 4096;
    pub fn flush(&mut self) {
        if self.at != 0 {
            match &mut self.output {
                OutputDest::Stdout(stdout) => {
                    stdout.write_all(&self.buf[..self.at]).unwrap();
                    stdout.flush().unwrap();
                }
                OutputDest::File(file) => {
                    file.write_all(&self.buf[..self.at]).unwrap();
                    file.flush().unwrap();
                }
                OutputDest::Buf(buf) => buf.extend_from_slice(&self.buf[..self.at]),
                OutputDest::Delegate(delegate) => {
                    delegate.write_all(&self.buf[..self.at]).unwrap();
                    delegate.flush().unwrap();
                }
            }
            self.at = 0;
        }
    }
    pub fn print<T: Writable>(&mut self, s: T) {
        s.write(self);
    }
    pub fn print_line<T: Writable>(&mut self, s: T) {
        self.print(s);
        self.put(b'\n');
    }
    pub fn put(&mut self, b: u8) {
        self.buf[self.at] = b;
        self.at += 1;
        if self.at == self.buf.len() {
            self.flush();
        }
    }
    pub fn print_per_line<T: Writable>(&mut self, arg: &[T]) {
        self.print_per_line_iter(arg.iter());
    }
    pub fn print_iter<T: Writable, I: Iterator<Item = T>>(&mut self, iter: I) {
        let mut first = true;
        for e in iter {
            if first {
                first = false;
            } else {
                self.put(self.separator);
            }
            e.write(self);
        }
    }
    pub fn print_line_iter<T: Writable, I: Iterator<Item = T>>(&mut self, iter: I) {
        self.print_iter(iter);
        self.put(b'\n');
    }
    pub fn print_per_line_iter<T: Writable, I: Iterator<Item = T>>(&mut self, iter: I) {
        for e in iter {
            e.write(self);
            self.put(b'\n');
        }
    }
    pub fn set_bool_output(&mut self, bool_output: BoolOutput) {
        self.bool_output = bool_output;
    }
    pub fn set_precision(&mut self, precision: usize) {
        self.precision = Some(precision);
    }
    pub fn reset_precision(&mut self) {
        self.precision = None;
    }
    pub fn get_precision(&self) -> Option<usize> {
        self.precision
    }
    pub fn separator(&self) -> u8 {
        self.separator
    }
    pub fn set_separator(&mut self, separator: u8) {
        self.separator = separator;
    }
}
impl Write for Output<'_> {
    fn write(&mut self, buf: &[u8]) -> std::io::Result<usize> {
        let mut start = 0usize;
        let mut rem = buf.len();
        while rem > 0 {
            let len = (self.buf.len() - self.at).min(rem);
            self.buf[self.at..self.at + len].copy_from_slice(&buf[start..start + len]);
            self.at += len;
            if self.at == self.buf.len() {
                self.flush();
            }
            start += len;
            rem -= len;
        }
        Ok(buf.len())
    }
    fn flush(&mut self) -> std::io::Result<()> {
        self.flush();
        Ok(())
    }
}
pub trait Writable {
    fn write(&self, output: &mut Output);
}
impl Writable for &str {
    fn write(&self, output: &mut Output) {
        output.write_all(self.as_bytes()).unwrap();
    }
}
impl Writable for String {
    fn write(&self, output: &mut Output) {
        output.write_all(self.as_bytes()).unwrap();
    }
}
impl Writable for char {
    fn write(&self, output: &mut Output) {
        output.put(*self as u8);
    }
}
impl Writable for u8 {
    fn write(&self, output: &mut Output) {
        output.put(*self);
    }
}
impl<T: Writable> Writable for [T] {
    fn write(&self, output: &mut Output) {
        output.print_iter(self.iter());
    }
}
impl<T: Writable, const N: usize> Writable for [T; N] {
    fn write(&self, output: &mut Output) {
        output.print_iter(self.iter());
    }
}
impl<T: Writable + ?Sized> Writable for &T {
    fn write(&self, output: &mut Output) {
        T::write(self, output)
    }
}
impl<T: Writable> Writable for Vec<T> {
    fn write(&self, output: &mut Output) {
        self.as_slice().write(output);
    }
}
impl Writable for () {
    fn write(&self, _output: &mut Output) {}
}
macro_rules! write_to_string {
    ($($t:ident)+) => {
        $(impl Writable for $t { fn write(& self, output : & mut Output) { self
        .to_string().write(output); } })+
    };
}
write_to_string!(u16 u32 u64 u128 usize i8 i16 i32 i64 i128 isize);
macro_rules! tuple_writable {
    ($name0:ident $($name:ident : $id:tt)*) => {
        impl <$name0 : Writable, $($name : Writable,)*> Writable for ($name0, $($name,)*)
        { fn write(& self, out : & mut Output) { self.0.write(out); $(out.put(out
        .separator); self.$id .write(out);)* } }
    };
}
tuple_writable! {
    T
}
tuple_writable! {
    T U : 1
}
tuple_writable! {
    T U : 1 V : 2
}
tuple_writable! {
    T U : 1 V : 2 X : 3
}
tuple_writable! {
    T U : 1 V : 2 X : 3 Y : 4
}
tuple_writable! {
    T U : 1 V : 2 X : 3 Y : 4 Z : 5
}
tuple_writable! {
    T U : 1 V : 2 X : 3 Y : 4 Z : 5 A : 6
}
tuple_writable! {
    T U : 1 V : 2 X : 3 Y : 4 Z : 5 A : 6 B : 7
}
tuple_writable! {
    T U : 1 V : 2 X : 3 Y : 4 Z : 5 A : 6 B : 7 C : 8
}
impl<T: Writable> Writable for Option<T> {
    fn write(&self, output: &mut Output) {
        match self {
            None => (-1).write(output),
            Some(t) => t.write(output),
        }
    }
}
impl Writable for bool {
    fn write(&self, output: &mut Output) {
        let bool_output = output.bool_output;
        bool_output.output(output, *self)
    }
}
impl<T: Writable> Writable for Reverse<T> {
    fn write(&self, output: &mut Output) {
        self.0.write(output);
    }
}
}
}
pub mod misc {
pub mod recursive_function {
use std::marker::PhantomData;
macro_rules! recursive_function {
    ($name:ident, $trait:ident, ($($type:ident $arg:ident,)*)) => {
        pub trait $trait <$($type,)* Output > { fn call(& mut self, $($arg : $type,)*) ->
        Output; } pub struct $name < F, $($type,)* Output > where F : FnMut(& mut dyn
        $trait <$($type,)* Output >, $($type,)*) -> Output, { f : std::cell::UnsafeCell <
        F >, $($arg : PhantomData <$type >,)* phantom_output : PhantomData < Output >, }
        impl < F, $($type,)* Output > $name < F, $($type,)* Output > where F : FnMut(&
        mut dyn $trait <$($type,)* Output >, $($type,)*) -> Output, { pub fn new(f : F)
        -> Self { Self { f : std::cell::UnsafeCell::new(f), $($arg :
        Default::default(),)* phantom_output : Default::default(), } } } impl < F,
        $($type,)* Output > $trait <$($type,)* Output > for $name < F, $($type,)* Output
        > where F : FnMut(& mut dyn $trait <$($type,)* Output >, $($type,)*) -> Output, {
        fn call(& mut self, $($arg : $type,)*) -> Output { unsafe { (* self.f.get())
        (self, $($arg,)*) } } }
    };
}
recursive_function!(RecursiveFunction0, Callable0, ());
recursive_function!(RecursiveFunction, Callable, (Arg arg,));
recursive_function!(RecursiveFunction2, Callable2, (Arg1 arg1, Arg2 arg2,));
recursive_function!(RecursiveFunction3, Callable3, (Arg1 arg1, Arg2 arg2, Arg3 arg3,));
recursive_function!(
    RecursiveFunction4, Callable4, (Arg1 arg1, Arg2 arg2, Arg3 arg3, Arg4 arg4,)
);
recursive_function!(
    RecursiveFunction5, Callable5, (Arg1 arg1, Arg2 arg2, Arg3 arg3, Arg4 arg4, Arg5
    arg5,)
);
recursive_function!(
    RecursiveFunction6, Callable6, (Arg1 arg1, Arg2 arg2, Arg3 arg3, Arg4 arg4, Arg5
    arg5, Arg6 arg6,)
);
recursive_function!(
    RecursiveFunction7, Callable7, (Arg1 arg1, Arg2 arg2, Arg3 arg3, Arg4 arg4, Arg5
    arg5, Arg6 arg6, Arg7 arg7,)
);
recursive_function!(
    RecursiveFunction8, Callable8, (Arg1 arg1, Arg2 arg2, Arg3 arg3, Arg4 arg4, Arg5
    arg5, Arg6 arg6, Arg7 arg7, Arg8 arg8,)
);
recursive_function!(
    RecursiveFunction9, Callable9, (Arg1 arg1, Arg2 arg2, Arg3 arg3, Arg4 arg4, Arg5
    arg5, Arg6 arg6, Arg7 arg7, Arg8 arg8, Arg9 arg9,)
);
}
pub mod test_type {
pub enum TestType {
    Single,
    MultiNumber,
    MultiEof,
}
pub enum TaskType {
    Classic,
    Interactive,
}
}
}
pub mod numbers {
pub mod num_traits {
pub mod algebra {
use crate::algo_lib::numbers::num_traits::invertible::Invertible;
use std::ops::{
    Add, AddAssign, Div, DivAssign, Mul, MulAssign, Neg, Rem, RemAssign, Sub, SubAssign,
};
pub trait Zero {
    fn zero() -> Self;
}
pub trait One {
    fn one() -> Self;
}
pub trait AdditionMonoid: Add<Output = Self> + AddAssign + Zero + Eq + Sized {}
impl<T: Add<Output = Self> + AddAssign + Zero + Eq> AdditionMonoid for T {}
pub trait AdditionMonoidWithSub: AdditionMonoid + Sub<Output = Self> + SubAssign {}
impl<T: AdditionMonoid + Sub<Output = Self> + SubAssign> AdditionMonoidWithSub for T {}
pub trait AdditionGroup: AdditionMonoidWithSub + Neg<Output = Self> {}
impl<T: AdditionMonoidWithSub + Neg<Output = Self>> AdditionGroup for T {}
pub trait MultiplicationMonoid: Mul<Output = Self> + MulAssign + One + Eq + Sized {}
impl<T: Mul<Output = Self> + MulAssign + One + Eq> MultiplicationMonoid for T {}
pub trait IntegerMultiplicationMonoid: MultiplicationMonoid + Div<
        Output = Self,
    > + Rem<Output = Self> + DivAssign + RemAssign {}
impl<
    T: MultiplicationMonoid + Div<Output = Self> + Rem<Output = Self> + DivAssign
        + RemAssign,
> IntegerMultiplicationMonoid for T {}
pub trait MultiplicationGroup: MultiplicationMonoid + Div<
        Output = Self,
    > + DivAssign + Invertible<Output = Self> {}
impl<
    T: MultiplicationMonoid + Div<Output = Self> + DivAssign + Invertible<Output = Self>,
> MultiplicationGroup for T {}
pub trait SemiRing: AdditionMonoid + MultiplicationMonoid {}
impl<T: AdditionMonoid + MultiplicationMonoid> SemiRing for T {}
pub trait SemiRingWithSub: AdditionMonoidWithSub + SemiRing {}
impl<T: AdditionMonoidWithSub + SemiRing> SemiRingWithSub for T {}
pub trait Ring: SemiRing + AdditionGroup {}
impl<T: SemiRing + AdditionGroup> Ring for T {}
pub trait IntegerSemiRing: SemiRing + IntegerMultiplicationMonoid {}
impl<T: SemiRing + IntegerMultiplicationMonoid> IntegerSemiRing for T {}
pub trait IntegerSemiRingWithSub: SemiRingWithSub + IntegerSemiRing {}
impl<T: SemiRingWithSub + IntegerSemiRing> IntegerSemiRingWithSub for T {}
pub trait IntegerRing: IntegerSemiRing + Ring {}
impl<T: IntegerSemiRing + Ring> IntegerRing for T {}
pub trait Field: Ring + MultiplicationGroup {}
impl<T: Ring + MultiplicationGroup> Field for T {}
macro_rules! zero_one_integer_impl {
    ($($t:ident)+) => {
        $(impl Zero for $t { fn zero() -> Self { 0 } } impl One for $t { fn one() -> Self
        { 1 } })+
    };
}
zero_one_integer_impl!(i128 i64 i32 i16 i8 isize u128 u64 u32 u16 u8 usize);
}
pub mod invertible {
pub trait Invertible {
    type Output;
    fn inv(&self) -> Option<Self::Output>;
}
}
}
}
}