// 
pub mod solution {

use crate::collections::iter_ext::collect::IterCollect;
use crate::collections::iter_ext::iters::Iters;
use crate::collections::min_max::MinimMaxim;
use crate::collections::segment_tree::{SegmentTree, SegmentTreeNode};
use crate::io::input::Input;
use crate::io::output::Output;

type PreCalc = ();

fn solve(input: &mut Input, out: &mut Output, _test_case: usize, _data: &PreCalc) {
    let n = input.read_size();
    let a = input.read_long_vec(n);

    #[derive(Copy, Clone, Default)]
    struct Node {
        max: i64,
        min: i64,
    }

    impl SegmentTreeNode for Node {
        fn new(_left: usize, _right: usize) -> Self {
            Self {
                min: i64::MAX / 2,
                max: 0,
            }
        }

        fn join(
            &mut self,
            left_val: &Self,
            right_val: &Self,
            _left: usize,
            _mid: usize,
            _right: usize,
        ) {
            self.max = left_val.max.max(right_val.max);
            self.min = left_val.min.min(right_val.min);
        }

        fn accumulate(&mut self, _value: &Self, _left: usize, _right: usize) {}

        fn reset_delta(&mut self, _left: usize, _right: usize) {}
    }

    let mut st = SegmentTree::from_generator(n, |i| Node {
        max: a[i],
        min: a[i],
    });
    let mut order = (0..n).collect_vec();
    order.sort_by_key(|&i| a[i]);
    let mut left = n;
    let mut right = 0;
    let mut ans = None;
    for &i in &order {
        left.minim(i);
        right.maxim(i);
        let Node {
            min: in_min,
            max: in_max,
        } = st.query(left..=right);
        let Node {
            min: left_min,
            max: left_max,
        } = st.query(..left);
        let Node {
            min: right_min,
            max: right_max,
        } = st.query(right + 1..);
        let out_min = left_min.min(right_min);
        let out_max = left_max.max(right_max);
        let cur = (in_max - in_min).max(out_max - out_min);
        ans.minim(cur);
    }
    left = n;
    right = 0;
    for &i in order.rev() {
        left.minim(i);
        right.maxim(i);
        let Node {
            min: in_min,
            max: in_max,
        } = st.query(left..=right);
        let Node {
            min: left_min,
            max: left_max,
        } = st.query(..left);
        let Node {
            min: right_min,
            max: right_max,
        } = st.query(right + 1..);
        let out_min = left_min.min(right_min);
        let out_max = left_max.max(right_max);
        let cur = (in_max - in_min).max(out_max - out_min);
        ans.minim(cur);
    }
    out.print_line(ans);
}

pub(crate) fn run(mut input: Input, mut output: Output) -> bool {
    let pre_calc = ();

    #[allow(dead_code)]
    enum TestType {
        Single,
        MultiNumber,
        MultiEof,
    }
    let test_type = TestType::MultiNumber;
    match test_type {
        TestType::Single => solve(&mut input, &mut output, 1, &pre_calc),
        TestType::MultiNumber => {
            let t = input.read();
            for i in 1..=t {
                solve(&mut input, &mut output, i, &pre_calc);
            }
        }
        TestType::MultiEof => {
            let mut i = 1;
            while input.peek().is_some() {
                solve(&mut input, &mut output, i, &pre_calc);
                i += 1;
            }
        }
    }
    output.flush();
    input.skip_whitespace();
    input.peek().is_none()
}

}
pub mod collections {
pub mod bounds {
use std::ops::RangeBounds;

pub fn clamp(range: impl RangeBounds<usize>, n: usize) -> (usize, usize) {
    let start = match range.start_bound() {
        std::ops::Bound::Included(&x) => x,
        std::ops::Bound::Excluded(&x) => x + 1,
        std::ops::Bound::Unbounded => 0,
    };
    let end = match range.end_bound() {
        std::ops::Bound::Included(&x) => x + 1,
        std::ops::Bound::Excluded(&x) => x,
        std::ops::Bound::Unbounded => n,
    };
    (start, end.min(n))
}
}
pub mod iter_ext {
pub mod collect {
pub trait IterCollect<T>: Iterator<Item = T> + Sized {
    fn collect_vec(self) -> Vec<T> {
        self.collect()
    }
}

impl<T, I: Iterator<Item = T> + Sized> IterCollect<T> for I {}
}
pub mod iters {
use std::iter::{Chain, Enumerate, Rev, Skip, Zip};

pub trait Iters<'a>: 'a
where
    &'a Self: IntoIterator,
{
    fn enumerate(&'a self) -> Enumerate<<&'a Self as IntoIterator>::IntoIter>;
    fn rev(&'a self) -> Rev<<&'a Self as IntoIterator>::IntoIter>
    where
        <&'a Self as IntoIterator>::IntoIter: DoubleEndedIterator;
    fn skip(&'a self, n: usize) -> Skip<<&'a Self as IntoIterator>::IntoIter>;
    fn chain<V: 'a>(
        &'a self,
        chained: &'a V,
    ) -> Chain<<&'a Self as IntoIterator>::IntoIter, <&'a V as IntoIterator>::IntoIter>
    where
        &'a V: IntoIterator<Item = <&'a Self as IntoIterator>::Item>;
    fn zip<V: 'a>(
        &'a self,
        other: &'a V,
    ) -> Zip<<&'a Self as IntoIterator>::IntoIter, <&'a V as IntoIterator>::IntoIter>
    where
        &'a V: IntoIterator<Item = <&'a Self as IntoIterator>::Item>;
}

impl<'a, U: 'a> Iters<'a> for U
where
    &'a U: IntoIterator,
{
    fn enumerate(&'a self) -> Enumerate<<&'a Self as IntoIterator>::IntoIter> {
        self.into_iter().enumerate()
    }

    fn rev(&'a self) -> Rev<<&'a Self as IntoIterator>::IntoIter>
    where
        <&'a Self as IntoIterator>::IntoIter: DoubleEndedIterator,
    {
        self.into_iter().rev()
    }

    fn skip(&'a self, n: usize) -> Skip<<&'a Self as IntoIterator>::IntoIter> {
        self.into_iter().skip(n)
    }

    fn chain<V: 'a>(
        &'a self,
        chained: &'a V,
    ) -> Chain<<&'a Self as IntoIterator>::IntoIter, <&'a V as IntoIterator>::IntoIter>
    where
        &'a V: IntoIterator<Item = <&'a Self as IntoIterator>::Item>,
    {
        self.into_iter().chain(chained)
    }

    fn zip<V: 'a>(
        &'a self,
        other: &'a V,
    ) -> Zip<<&'a Self as IntoIterator>::IntoIter, <&'a V as IntoIterator>::IntoIter>
    where
        &'a V: IntoIterator<Item = <&'a Self as IntoIterator>::Item>,
    {
        self.into_iter().zip(other)
    }
}
}
}
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 segment_tree {
use crate::collections::bounds::clamp;
use crate::misc::direction::Direction;
use crate::when;
use std::marker::PhantomData;
use std::ops::RangeBounds;

pub trait SegmentTreeNode {
    fn new(left: usize, right: usize) -> Self;
    fn join(&mut self, left_val: &Self, right_val: &Self, left: usize, mid: usize, right: usize);
    fn accumulate(&mut self, value: &Self, left: usize, right: usize);
    fn reset_delta(&mut self, left: usize, right: usize);
}

pub trait Pushable<T>: SegmentTreeNode {
    fn push(&mut self, delta: T, left: usize, right: usize);
}

impl<T: SegmentTreeNode> Pushable<&T> for T {
    fn push(&mut self, delta: &T, left: usize, right: usize) {
        self.accumulate(delta, left, right);
    }
}

pub trait QueryResult<Result>: SegmentTreeNode {
    fn empty_result() -> Result;
    fn result(&self) -> Result;
    fn join_results(
        left_res: Result,
        right_res: Result,
        left: usize,
        mid: usize,
        right: usize,
    ) -> Result;
}

impl<T: SegmentTreeNode + Clone> QueryResult<T> for T {
    fn empty_result() -> T {
        Self::new(0, 0)
    }

    fn result(&self) -> T {
        self.clone()
    }

    fn join_results(left_res: T, right_res: T, left: usize, mid: usize, right: usize) -> T {
        when! {
            left == mid => right_res,
            right == mid => left_res,
            else => {
                let mut res = Self::new(left, right);
                res.join(&left_res, &right_res, left, mid, right);
                res
            },
        }
    }
}

#[derive(Clone)]
pub struct SegmentTree<Node> {
    n: usize,
    nodes: Vec<Node>,
}

impl<Node: SegmentTreeNode> SegmentTree<Node> {
    pub fn new(n: usize) -> Self {
        Self::from_generator(n, |left| Node::new(left, left + 1))
    }

    pub fn from_array(arr: Vec<Node>) -> Self {
        let n = arr.len();
        let mut iter = arr.into_iter();
        Self::from_generator(n, |_| iter.next().unwrap())
    }

    pub fn from_generator<F>(n: usize, gen: F) -> Self
    where
        F: FnMut(usize) -> Node,
    {
        if n == 0 {
            panic!("Empty seg trees not allowed");
        }
        let mut res = Self {
            n,
            nodes: Vec::with_capacity(2 * n - 1),
        };
        res.init(gen);
        res
    }

    fn init<F>(&mut self, mut f: F)
    where
        F: FnMut(usize) -> Node,
    {
        self.init_impl(2 * self.n - 2, 0, self.n, &mut f);
    }

    fn init_impl<F>(&mut self, root: usize, left: usize, right: usize, f: &mut F)
    where
        F: FnMut(usize) -> Node,
    {
        if left + 1 == right {
            self.nodes.push(f(left));
        } else {
            let mid = left + ((right - left) >> 1);
            let left_child = root - 2 * (right - mid);
            let right_child = root - 1;
            self.init_impl(left_child, left, mid, f);
            self.init_impl(right_child, mid, right, f);
            let mut node = Node::new(left, right);
            node.join(
                &self.nodes[left_child],
                &self.nodes[right_child],
                left,
                mid,
                right,
            );
            self.nodes.push(node);
        }
    }

    pub fn point_query(&mut self, at: usize) -> &Node {
        assert!(at < self.n);
        self.do_point_query(2 * self.n - 2, 0, self.n, at)
    }

    fn do_point_query(&mut self, root: usize, left: usize, right: usize, at: usize) -> &Node {
        if left + 1 == right {
            &self.nodes[root]
        } else {
            let mid = (left + right) >> 1;
            self.push_down(root, left, mid, right);
            let left_child = root - 2 * (right - mid);
            let right_child = root - 1;
            if at < mid {
                self.do_point_query(left_child, left, mid, at)
            } else {
                self.do_point_query(right_child, mid, right, at)
            }
        }
    }

    pub fn point_update<T>(&mut self, at: usize, val: T)
    where
        Node: Pushable<T>,
    {
        assert!(at < self.n);
        self.do_point_update(2 * self.n - 2, 0, self.n, at, val);
    }

    fn do_point_update<T>(&mut self, root: usize, left: usize, right: usize, at: usize, val: T)
    where
        Node: Pushable<T>,
    {
        if left + 1 == right {
            self.nodes[root].push(val, left, right);
        } else {
            let mid = (left + right) >> 1;
            self.push_down(root, left, mid, right);
            let left_child = root - 2 * (right - mid);
            let right_child = root - 1;
            if at < mid {
                self.do_point_update(left_child, left, mid, at, val);
            } else {
                self.do_point_update(right_child, mid, right, at, val);
            }
            self.join(root, left, mid, right);
        }
    }

    pub fn point_through_update<'a, T>(&mut self, at: usize, val: &'a T)
    where
        Node: Pushable<&'a T>,
    {
        assert!(at < self.n);
        self.do_point_through_update(2 * self.n - 2, 0, self.n, at, val);
    }

    fn do_point_through_update<'a, T>(
        &mut self,
        root: usize,
        left: usize,
        right: usize,
        at: usize,
        val: &'a T,
    ) where
        Node: Pushable<&'a T>,
    {
        self.nodes[root].push(val, left, right);
        if left + 1 != right {
            let mid = (left + right) >> 1;
            self.push_down(root, left, mid, right);
            let left_child = root - 2 * (right - mid);
            let right_child = root - 1;
            if at < mid {
                self.do_point_update(left_child, left, mid, at, val);
            } else {
                self.do_point_update(right_child, mid, right, at, val);
            }
        }
    }

    pub fn point_operation<Args, Res>(
        &mut self,
        op: &mut dyn PointOperation<Node, Args, Res>,
        args: Args,
    ) -> Res {
        self.do_point_operation(op, 2 * self.n - 2, 0, self.n, args)
    }

    fn do_point_operation<Args, Res>(
        &mut self,
        op: &mut dyn PointOperation<Node, Args, Res>,
        root: usize,
        left: usize,
        right: usize,
        args: Args,
    ) -> Res {
        if left + 1 == right {
            op.adjust_leaf(&mut self.nodes[root], left, args)
        } else {
            let mid = (left + right) >> 1;
            self.push_down(root, left, mid, right);
            let left_child = root - 2 * (right - mid);
            let right_child = root - 1;
            let (l, r) = self.nodes.split_at_mut(root);
            let (l, m) = l.split_at_mut(right_child);
            let direction = op.select_branch(
                &mut r[0],
                &mut l[left_child],
                &mut m[0],
                &args,
                left,
                mid,
                right,
            );
            let res = match direction {
                Direction::Left => self.do_point_operation(op, left_child, left, mid, args),
                Direction::Right => self.do_point_operation(op, right_child, mid, right, args),
            };
            self.join(root, left, mid, right);
            res
        }
    }

    pub fn update<'a, T>(&mut self, range: impl RangeBounds<usize>, val: &'a T)
    where
        Node: Pushable<&'a T>,
    {
        let (from, to) = clamp(range, self.n);
        self.do_update(2 * self.n - 2, 0, self.n, from, to, val)
    }

    pub fn do_update<'a, T>(
        &mut self,
        root: usize,
        left: usize,
        right: usize,
        from: usize,
        to: usize,
        val: &'a T,
    ) where
        Node: Pushable<&'a T>,
    {
        when! {
            left >= to || right <= from => {},
            left >= from && right <= to => self.nodes[root].push(val, left, right),
            else => {
                let mid = (left + right) >> 1;
                self.push_down(root, left, mid, right);
                let left_child = root - 2 * (right - mid);
                let right_child = root - 1;
                self.do_update(left_child, left, mid, from, to, val);
                self.do_update(right_child, mid, right, from, to, val);
                self.join(root, left, mid, right);
            },
        }
    }

    pub fn operation<Args, Res>(
        &mut self,
        range: impl RangeBounds<usize>,
        op: &mut dyn Operation<Node, Args, Res>,
        args: &Args,
    ) -> Res {
        let (from, to) = clamp(range, self.n);
        self.do_operation(2 * self.n - 2, 0, self.n, from, to, op, args)
    }

    pub fn do_operation<Args, Res>(
        &mut self,
        root: usize,
        left: usize,
        right: usize,
        from: usize,
        to: usize,
        op: &mut dyn Operation<Node, Args, Res>,
        args: &Args,
    ) -> Res {
        when! {
            left >= to || right <= from => op.empty_result(left, right, args),
            left >= from && right <= to => op.process_result(&mut self.nodes[root], args),
            else => {
                let mid = (left + right) >> 1;
                self.push_down(root, left, mid, right);
                let left_child = root - 2 * (right - mid);
                let right_child = root - 1;
                let left_result = self.do_operation(left_child, left, mid, from, to, op, args);
                let right_result = self.do_operation(right_child, mid, right, from, to, op, args);
                self.join(root, left, mid, right);
                op.join_results(left_result, right_result, args)
            },
        }
    }

    pub fn binary_search<Res>(
        &mut self,
        wh: impl FnMut(&Node, &Node) -> Direction,
        calc: impl FnMut(&Node, usize) -> Res,
    ) -> Res {
        self.do_binary_search(2 * self.n - 2, 0, self.n, wh, calc)
    }

    fn do_binary_search<Res>(
        &mut self,
        root: usize,
        left: usize,
        right: usize,
        mut wh: impl FnMut(&Node, &Node) -> Direction,
        mut calc: impl FnMut(&Node, usize) -> Res,
    ) -> Res {
        if left + 1 == right {
            calc(&self.nodes[root], left)
        } else {
            let mid = (left + right) >> 1;
            self.push_down(root, left, mid, right);
            let left_child = root - 2 * (right - mid);
            let right_child = root - 1;
            let direction = wh(&self.nodes[left_child], &self.nodes[right_child]);
            match direction {
                Direction::Left => self.do_binary_search(left_child, left, mid, wh, calc),
                Direction::Right => self.do_binary_search(right_child, mid, right, wh, calc),
            }
        }
    }

    fn join(&mut self, root: usize, left: usize, mid: usize, right: usize) {
        let left_child = root - 2 * (right - mid);
        let right_child = root - 1;
        let (left_node, right_node) = self.nodes.split_at_mut(root);
        right_node[0].join(
            &left_node[left_child],
            &left_node[right_child],
            left,
            mid,
            right,
        );
    }

    fn do_push_down(&mut self, parent: usize, to: usize, left: usize, right: usize) {
        let (left_nodes, right_nodes) = self.nodes.split_at_mut(parent);
        left_nodes[to].accumulate(&right_nodes[0], left, right);
    }

    fn push_down(&mut self, root: usize, left: usize, mid: usize, right: usize) {
        self.do_push_down(root, root - 2 * (right - mid), left, mid);
        self.do_push_down(root, root - 1, mid, right);
        self.nodes[root].reset_delta(left, right);
    }
}

impl<Node: SegmentTreeNode + Clone> SegmentTree<Node> {
    pub fn query<T>(&mut self, range: impl RangeBounds<usize>) -> T
    where
        Node: QueryResult<T>,
    {
        let (from, to) = clamp(range, self.n);
        if from >= to {
            Node::empty_result()
        } else {
            self.do_query(2 * self.n - 2, 0, self.n, from, to)
        }
    }

    fn do_query<T>(&mut self, root: usize, left: usize, right: usize, from: usize, to: usize) -> T
    where
        Node: QueryResult<T>,
    {
        if left >= from && right <= to {
            self.nodes[root].result()
        } else {
            let mid = (left + right) >> 1;
            self.push_down(root, left, mid, right);
            let left_child = root - 2 * (right - mid);
            let right_child = root - 1;
            when! {
                to <= mid => self.do_query(left_child, left, mid, from, to),
                from >= mid => self.do_query(right_child, mid, right, from, to),
                else => {
                    let left_result = self.do_query(left_child, left, mid, from, to);
                    let right_result = self.do_query(right_child, mid, right, from, to);
                    Node::join_results(left_result, right_result, left, mid, right)
                },
            }
        }
    }
}

pub trait PointOperation<Node: SegmentTreeNode, Args, Res = Node> {
    fn adjust_leaf(&mut self, leaf: &mut Node, at: usize, args: Args) -> Res;
    fn select_branch(
        &mut self,
        root: &mut Node,
        left_child: &mut Node,
        right_child: &mut Node,
        args: &Args,
        left: usize,
        mid: usize,
        right: usize,
    ) -> Direction;
}

pub struct PointOperationClosure<'s, Node: SegmentTreeNode, Args, Res = Node> {
    adjust_leaf: Box<dyn FnMut(&mut Node, usize, Args) -> Res + 's>,
    select_branch: Box<
        dyn FnMut(&mut Node, &mut Node, &mut Node, &Args, usize, usize, usize) -> Direction + 's,
    >,
    phantom_node: PhantomData<Node>,
    phantom_args: PhantomData<Args>,
    phantom_res: PhantomData<Res>,
}

impl<'s, Node: SegmentTreeNode, Args, Res> PointOperationClosure<'s, Node, Args, Res> {
    pub fn new<F1, F2>(adjust_leaf: F1, select_branch: F2) -> Self
    where
        F1: FnMut(&mut Node, usize, Args) -> Res + 's,
        F2: FnMut(&mut Node, &mut Node, &mut Node, &Args, usize, usize, usize) -> Direction + 's,
    {
        Self {
            adjust_leaf: Box::new(adjust_leaf),
            select_branch: Box::new(select_branch),
            phantom_node: Default::default(),
            phantom_args: Default::default(),
            phantom_res: Default::default(),
        }
    }
}

impl<'s, Node: SegmentTreeNode, Args, Res> PointOperation<Node, Args, Res>
    for PointOperationClosure<'s, Node, Args, Res>
{
    fn adjust_leaf(&mut self, leaf: &mut Node, at: usize, args: Args) -> Res {
        (self.adjust_leaf)(leaf, at, args)
    }

    fn select_branch(
        &mut self,
        root: &mut Node,
        left_child: &mut Node,
        right_child: &mut Node,
        args: &Args,
        left: usize,
        mid: usize,
        right: usize,
    ) -> Direction {
        (self.select_branch)(root, left_child, right_child, args, left, mid, right)
    }
}

pub trait Operation<Node: SegmentTreeNode, Args, Res = Node> {
    fn process_result(&mut self, node: &mut Node, args: &Args) -> Res;
    fn join_results(&mut self, left_res: Res, right_res: Res, args: &Args) -> Res;
    fn empty_result(&mut self, left: usize, right: usize, args: &Args) -> Res;
}

pub struct OperationClosure<'s, Node: SegmentTreeNode, Args, Res = Node> {
    process_result: Box<dyn FnMut(&mut Node, &Args) -> Res + 's>,
    join_results: Box<dyn FnMut(Res, Res, &Args) -> Res + 's>,
    empty_result: Box<dyn FnMut(usize, usize, &Args) -> Res + 's>,
    phantom_node: PhantomData<Node>,
    phantom_args: PhantomData<Args>,
    phantom_res: PhantomData<Res>,
}

impl<'s, Node: SegmentTreeNode, Args, Res> OperationClosure<'s, Node, Args, Res> {
    pub fn new<F1, F2, F3>(process_result: F1, join_results: F2, empty_result: F3) -> Self
    where
        F1: FnMut(&mut Node, &Args) -> Res + 's,
        F2: FnMut(Res, Res, &Args) -> Res + 's,
        F3: FnMut(usize, usize, &Args) -> Res + 's,
    {
        Self {
            process_result: Box::new(process_result),
            join_results: Box::new(join_results),
            empty_result: Box::new(empty_result),
            phantom_node: Default::default(),
            phantom_args: Default::default(),
            phantom_res: Default::default(),
        }
    }
}

impl<'s, Node: SegmentTreeNode, Args, Res> Operation<Node, Args, Res>
    for OperationClosure<'s, Node, Args, Res>
{
    fn process_result(&mut self, node: &mut Node, args: &Args) -> Res {
        (self.process_result)(node, args)
    }

    fn join_results(&mut self, left_res: Res, right_res: Res, args: &Args) -> Res {
        (self.join_results)(left_res, right_res, args)
    }

    fn empty_result(&mut self, left: usize, right: usize, args: &Args) -> Res {
        (self.empty_result)(left, right, args)
    }
}
}
pub mod vec_ext {
pub mod default {
pub fn default_vec<T: Default>(len: usize) -> Vec<T> {
    let mut v = Vec::with_capacity(len);
    for _ in 0..len {
        v.push(T::default());
    }
    v
}
}
}
}
pub mod io {
pub mod input {
use crate::collections::vec_ext::default::default_vec;
use std::io::Read;

pub struct Input<'s> {
    input: &'s mut dyn Read,
    buf: Vec<u8>,
    at: usize,
    buf_read: usize,
}

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<'s> Input<'s> {
    const DEFAULT_BUF_SIZE: usize = 4096;

    pub fn new(input: &'s mut dyn Read) -> Self {
        Self {
            input,
            buf: default_vec(Self::DEFAULT_BUF_SIZE),
            at: 0,
            buf_read: 0,
        }
    }

    pub fn new_with_size(input: &'s mut dyn Read, buf_size: usize) -> Self {
        Self {
            input,
            buf: default_vec(buf_size),
            at: 0,
            buf_read: 0,
        }
    }

    pub fn get(&mut self) -> Option<u8> {
        if self.refill_buffer() {
            let res = self.buf[self.at];
            self.at += 1;
            if res == b'\r' {
                if self.refill_buffer() && self.buf[self.at] == b'\n' {
                    self.at += 1;
                }
                return Some(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 !char::from(b).is_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 char::from(c).is_whitespace() {
                break;
            }
            res.push(c);
        }
        if res.is_empty() {
            None
        } else {
            Some(res)
        }
    }

    //noinspection RsSelfConvention
    pub fn is_exhausted(&mut self) -> bool {
        self.peek().is_none()
    }

    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) -> char {
        self.skip_whitespace();
        self.get().unwrap().into()
    }

    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 = self.input.read(&mut self.buf).unwrap();
            self.buf_read != 0
        } else {
            true
        }
    }
}

pub trait Readable {
    fn read(input: &mut Input) -> Self;
}

impl Readable for char {
    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)
    }
}

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 u8 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}

impl Read for Input<'_> {
    fn read(&mut self, buf: &mut [u8]) -> std::io::Result<usize> {
        if self.at == self.buf_read {
            self.input.read(buf)
        } else {
            let mut i = 0;
            while i < buf.len() && self.at < self.buf_read {
                buf[i] = self.buf[self.at];
                i += 1;
                self.at += 1;
            }
            Ok(i)
        }
    }
}
}
pub mod output {
use crate::collections::vec_ext::default::default_vec;
use std::io::{stderr, Stderr, 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,
        }
    }
}

pub struct Output<'s> {
    output: &'s mut dyn Write,
    buf: Vec<u8>,
    at: usize,
    auto_flush: bool,
    bool_output: BoolOutput,
}

impl<'s> Output<'s> {
    const DEFAULT_BUF_SIZE: usize = 4096;

    pub fn new(output: &'s mut dyn Write) -> Self {
        Self {
            output,
            buf: default_vec(Self::DEFAULT_BUF_SIZE),
            at: 0,
            auto_flush: false,
            bool_output: BoolOutput::YesNoCaps,
        }
    }

    pub fn new_with_auto_flush(output: &'s mut dyn Write) -> Self {
        Self {
            output,
            buf: default_vec(Self::DEFAULT_BUF_SIZE),
            at: 0,
            auto_flush: true,
            bool_output: BoolOutput::YesNoCaps,
        }
    }

    pub fn flush(&mut self) {
        if self.at != 0 {
            self.output.write_all(&self.buf[..self.at]).unwrap();
            self.output.flush().unwrap();
            self.at = 0;
        }
    }

    pub fn print<T: Writable>(&mut self, s: T) {
        s.write(self);
        self.maybe_flush();
    }

    pub fn print_line<T: Writable>(&mut self, s: T) {
        self.print(s);
        self.put(b'\n');
        self.maybe_flush();
    }

    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 maybe_flush(&mut self) {
        if self.auto_flush {
            self.flush();
        }
    }

    pub fn print_per_line<T: Writable>(&mut self, arg: &[T]) {
        for i in arg {
            i.write(self);
            self.put(b'\n');
        }
    }

    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(b' ');
            }
            e.write(self);
        }
    }

    pub fn print_iter_ref<'a, T: 'a + Writable, I: Iterator<Item = &'a T>>(&mut self, iter: I) {
        let mut first = true;
        for e in iter {
            if first {
                first = false;
            } else {
                self.put(b' ');
            }
            e.write(self);
        }
    }

    pub fn set_bool_output(&mut self, bool_output: BoolOutput) {
        self.bool_output = bool_output;
    }
}

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;
        }
        self.maybe_flush();
        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<T: Writable> Writable for [T] {
    fn write(&self, output: &mut Output) {
        output.print_iter_ref(self.iter());
    }
}

impl<T: Writable, const N: usize> Writable for [T; N] {
    fn write(&self, output: &mut Output) {
        output.print_iter_ref(self.iter());
    }
}

impl<T: Writable> 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!(u8 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);
                $(
                out.put(b' ');
                self.$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}

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)
    }
}

static mut ERR: Option<Stderr> = None;
pub fn err() -> Output<'static> {
    unsafe {
        if ERR.is_none() {
            ERR = Some(stderr());
        }
        Output::new_with_auto_flush(ERR.as_mut().unwrap())
    }
}
}
}
pub mod misc {
pub mod direction {
#[derive(Copy, Clone)]
pub enum Direction {
    Left,
    Right,
}
}
pub mod when {
#[macro_export]
macro_rules! when {
    {$($cond: expr => $then: expr,)*} => {
        match () {
            $(_ if $cond => $then,)*
            _ => unreachable!(),
        }
    };
    {$($cond: expr => $then: expr,)* else $(=>)? $else: expr,} => {
        match () {
            $(_ if $cond => $then,)*
            _ => $else,
        }
    };
}
}
}
fn main() {
    let mut sin = std::io::stdin();
    let input = if false {
        io::input::Input::new_with_size(&mut sin, 1)
    } else {
        io::input::Input::new(&mut sin)
    };

    let mut stdout = std::io::stdout();
    let output = if false {
        io::output::Output::new_with_auto_flush(&mut stdout)
    } else {
        io::output::Output::new(&mut stdout)
    };

    solution::run(input, output);
}