Problem:
Score : 500 points

Problem Statement

We have a deck consisting of N cards. Each card has an integer written on it. The integer on the i-th card from the top is a_i.

Two people X and Y will play a game using this deck. Initially, X has a card with Z written on it in his hand, and Y has a card with W written on it in his hand. Then, starting from X, they will alternately perform the following action:

Draw some number of cards from the top of the deck. Then, discard the card in his hand and keep the last drawn card instead. Here, at least one card must be drawn.

The game ends when there is no more card in the deck. The score of the game is the absolute difference of the integers written on the cards in the two players' hand.

X will play the game so that the score will be maximized, and Y will play the game so that the score will be minimized. What will be the score of the game?

Constraints

All input values are integers.

1 \leq N \leq 2000

1 \leq Z, W, a_i \leq 10^9

Input

Input is given from Standard Input in the following format:

N Z W
a_1 a_2 ... a_N

Output

Print the score.

Sample Input 1

3 100 100
10 1000 100

Sample Output 1

900

If X draws two cards first, Y will draw the last card, and the score will be |1000 - 100| = 900.

Sample Input 2

3 100 1000
10 100 100

Sample Output 2

900

If X draws all the cards first, the score will be |1000 - 100| = 900.

Sample Input 3

5 1 1
1 1 1 1 1

Sample Output 3

0

Sample Input 4

1 1 1
1000000000

Sample Output 4

999999999

Solution in C++14 (GCC 5.4.1) (judge verdict: Accepted)

///////////////////////////////////////////////////////////////////////////////

#include <bits/stdc++.h>
#include <unistd.h>
#include <time.h>
#include <sys/time.h>

using namespace std;

///////////////////////////////////////////////////////////////////////////////

#define DEBUG 0

#define pb push_back
#define V vector
#define M unordered_map
#define S static

#define rep(i,n) for(ll i=0LL;i<n;++i)
#define srep(i,s,n) for(ll i=s;i<n;++i)
#define rrep(i,n) for(ll i=n-1LL;i>=0LL;--i)
#define ALL(a) (a).begin(),(a).end()
#define CIN(x) do { \
    assert(!cin.eof()); \
    cin >> x; \
    assert(!cin.fail()); \
} while(0);
#if DEBUG
#define debug_print(...) _debug_print(__VA_ARGS__)
#define debug_printf(...) printf(__VA_ARGS__)
#define debug_print_time _debug_print_time
#else // DEBUG
#define debug_print(...)
#define debug_printf(...)
#define debug_print_time
#endif // DEBUG

typedef long long ll;
typedef unsigned long long ull;
typedef tuple<ll, ll> t2;
typedef tuple<ll, ll, ll> t3;
typedef tuple<ll, ll, ll, ll> t4;
typedef tuple<ll, ll, ll, ll, ll> t5;
template <typename T>
using priority_queue_incr = priority_queue<T, V<T>, greater<T>>;

///////////////////////////////////////////////////////////////////////////////

template <typename TT, typename T>
T get_m(M<TT, T> &m, TT k, T default_value)
{
    if (m.find(k) == m.end()) return m[k] = default_value;
    return m[k];
}

template <typename TT, typename T>
void incr_m(M<TT, T> &m, TT k)
{
    if (m.find(k) == m.end()) m[k] = 0;
    m[k]++;
}

struct UnionFind
{
    ull *parent, *count, *rank;

    UnionFind(ull n) {
        parent = new ull[n+1];
        count = new ull[n+1];
        rank = new ull[n+1];
        for (ull i = 0ULL; i < n+1; ++i) {
            parent[i] = i;
            count[i] = 1;
            rank[i] = 0;
        }
    }

    ~UnionFind() {
        delete rank;
        delete count;
        delete parent;
    }

    ull root(ull i) {
        if (parent[i] == i) return i;
        parent[i] = root(parent[i]);
        return parent[i];
    }

    void unite(ull i, ull j) {
        ull rooti = root(i);
        ull rootj = root(j);

        if (rooti == rootj) return;

        if (rank[rootj] < rank[rooti]) {
            parent[i] = parent[j] = parent[rootj] = rooti;
            count[rooti] += count[rootj];
        }
        else {
            parent[i] = parent[j] = parent[rooti] = rootj;
            count[rootj] += count[rooti];
            if (rank[rootj] == rank[rooti]) rank[rootj]++;
        }
    }

    bool same(ull i, ull j) {
        return root(i) == root(j);
    }
};

struct UnionFindM
{
    M<ull, ull> parent, count, rank;

    ull root(ull i) {
        ull parent_i = get_m(parent, i, i);
        if (parent_i == i) return i;
        return parent[i] = root(parent_i);
    }

    void unite(ull i, ull j) {
        ull rooti = root(i);
        ull rootj = root(j);

        if (rooti == rootj) return;

        if (get_m(rank, rootj, 0ULL) < get_m(rank, rooti, 0ULL)) {
            parent[i] = parent[j] = parent[rootj] = rooti;
            count[rooti] = get_m(count, rooti, 1ULL) + get_m(count, rootj, 1ULL);
        }
        else {
            parent[i] = parent[j] = parent[rooti] = rootj;
            count[rootj] = get_m(count, rootj, 1ULL) + get_m(count, rooti, 1ULL);
            if (get_m(rank, rootj, 0ULL) == get_m(rank, rooti, 0ULL)) rank[rootj]++;
        }
    }

    bool same(ull i, ull j) {
        return root(i) == root(j);
    }
};

struct BIT
{
    ll *tree;
    ll size;

    BIT(ll n, ll init) {
        tree = new ll[n+1];
        size = n;
        this->init(init);
    }

    void init(ll init) {
        memset(tree, 0, sizeof(ll) * (size+1));
        rep (i0, size) {
            ll idx = i0 + 1LL;
            while (idx <= size) {
                tree[idx] += init;
                idx += (idx & (-idx));
            }
        }
    }

    // idx is 1 origin
    void add(ll idx, ll x) {
        assert(idx > 0LL);
        while (idx <= size) {
            tree[idx] += x;
            idx += (idx & (-idx));
        }
    }

    // idx is 1 origin
    ll sum(ll idx) {
        assert(idx > 0LL);
        ll ret = 0LL;
        while (idx > 0LL) {
            ret += tree[idx];
            idx -= (idx & (-idx));
        }
        return ret;
    }
};

struct MaxFlow {
    V<ll> links[1005];
    ll capacities[1005][1005];
    ll nodes;

    MaxFlow(ll nodes) {
        // i == 0       --> S
        // i == nodes+1 --> T
        rep (i, nodes+2LL) links[i].clear();
        memset(capacities, 0, sizeof(capacities));
        this->nodes = nodes;
    }

    void add_path(ll a, ll b, ll capacity) {
        links[a].pb(b);
        links[b].pb(a);
        capacities[a][b] = capacity;
        capacities[b][a] = 0LL;
    }

    ll solve(void) {
        deque<V<ll>> q;
        ll ret = 0LL;

        for ( ; ; q.clear()) {

            V<ll> start;
            start.pb(0);
            q.push_front(start);

            bool checked[nodes+2];
            memset(checked, 0, sizeof(checked));

            V<ll> found;

            for ( ; !(q.empty()); ) {
                V<ll> path = q.front(); q.pop_front();
                ll last = path[path.size()-1];

                if (checked[last]) continue;
                if (last == nodes+1) {
                    found = path;
                    break;
                }

                checked[last] = true;
                for (auto next : (links[last])) {
                    if (capacities[last][next] == 0) continue;
                    V<ll> newpath(path);
                    newpath.pb(next);
                    q.push_front(newpath);
                }
            }

            if (found.size() == 0) {
                break;
            }
            else {
                ll flowcount = capacities[found[0]][found[1]];
                rep (i, found.size()-1) {
                    ll src = found[i];
                    ll dst = found[i+1];
                    flowcount = min(flowcount, capacities[src][dst]);
                }
                rep (i, found.size()-1) {
                    ll src = found[i];
                    ll dst = found[i+1];
                    capacities[src][dst] -= flowcount;
                    capacities[dst][src] += flowcount;
                }
                ret += flowcount;
            }
        }

        return ret;
    }
};

template <typename T>
struct SegmentTree {
    T *nodes;
    t2 *ranges;  // [start, end)
    ll nodecount;
    ll itemcount;
    T unit;
    T (*op)(T, T);

    SegmentTree(ll itemcount, T unit, T op(T, T)) {
        ll orig_itemcount = itemcount;
        this->itemcount = 1LL;
        while (this->itemcount < orig_itemcount) this->itemcount *= 2LL;
        nodecount = this->itemcount * 2 - 1;
        nodes = new T[nodecount];
        ranges = new t2[nodecount];
        this->unit = unit;
        this->op = op;

        ll start = 0LL;
        ll end = this->itemcount;
        ll len = this->itemcount;

        rep (i, nodecount) {
            nodes[i] = unit;
            ranges[i] = t2(start, end);
            if (end >= this->itemcount) {
                len /= 2LL;
                start = 0LL;
                end = len;
            }
            else {
                start = end;
                end = start + len;
            }
        }
    }

    void update(ll k, T v) {
        ll idx = k + itemcount - 1LL;
        nodes[idx] = v;
        idx = (idx - 1LL) / 2LL;

        for ( ; idx >= 0; idx = (idx - 1LL) / 2LL) {
            nodes[idx] = op(nodes[idx * 2LL + 1LL],
                            nodes[idx * 2LL + 2LL]);
            if (!idx) break;
        }
    }

    // query to [start, end)
    T query(ll start, ll end) const {
        return _query(start, end, 0LL);
    }

    T _query(ll start, ll end, ll idx) const {
        ll rstart = get<0>(ranges[idx]);
        ll rend = get<1>(ranges[idx]);

        if (start <= rstart && rend <= end) {
            return nodes[idx];
        }
        if (rend <= start || end <= rstart) {
            return unit;
        }
        T left = _query(start, end, idx * 2LL + 1LL);
        T right = _query(start, end, idx * 2LL + 2LL);
        return op(left, right);
    }

};

void llin(ll &a)
{
    CIN(a);
}

void llinl1(auto &v, ll count)
{
    for (ll i = 0LL; i < count ; ++i) {
        ll a;
        CIN(a);
        v.push_back(a);
    }
}

void llinl2(auto &v, ll count)
{
    for (ll i = 0LL; i < count ; ++i) {
        ll a, b;
        CIN(a >> b);
        v.push_back(t2(a, b));
    }
}

void llinl3(auto &v, ll count)
{
    for (ll i = 0LL; i < count ; ++i) {
        ll a, b, c;
        CIN(a >> b >> c);
        v.push_back(t3(a, b, c));
    }
}

void llinl4(auto &v, ll count)
{
    for (ll i = 0LL; i < count ; ++i) {
        ll a, b, c, d;
        CIN(a >> b >> c >> d);
        v.push_back(t4(a, b, c, d));
    }
}

void llina(auto &v, ll count)
{
    llinl1(v, count);
}

template <typename T>
T min(const V<T> v)
{
    T ret = v[0];
    for (auto i : v) ret = min(ret, i);
    return ret;
}

template <typename T>
T max(const V<T> v)
{
    T ret = v[0];
    for (auto i : v) ret = max(ret, i);
    return ret;
}

ll absll(ll x)
{
    if (x < 0) return -x;
    return x;
}

ll mod_mlt(ll x, ll y, ll mod)
{
    ll ret = 0LL;
    x %= mod;

    while (y) {
        if (y & 1LL) {
            ret += x;
            ret %= mod;
        }
        y >>= 1;
        x <<= 1;
        x %= mod;
    }

    return ret;
}

// O(log(exp))
ll mod_pow(ll base, ll exp, ll mod)
{
    ll ret = 1LL;

    for ( ; exp; ) {
        if (exp & 1LL) {
            ret *= base;
            ret %= mod;
        }
        base = (base * base) % mod;
        exp >>= 1;
    }

    return ret;
}

// O(log(mod))
ll mod_inv(ll x, ll mod)
{
    // available only when mod is prime
    return mod_pow(x, mod - 2LL, mod);
}

ll gcm(ll x, ll y)
{
    while (y != 0) {
        ll z = x % y;
        x = y;
        y = z;
    }
    return x;
}

template <typename T>
void sort(V<T> &v)
{
    sort(v.begin(), v.end());
}

template <typename T>
void sort_reverse(V<T> &v)
{
    sort(v.begin(), v.end(), greater<T>());
}

void get_divisors(V<ll> &retlist, ll x)
{
    for (ll i = 1LL; i < sqrt(x) + 3LL; ++i) {
        if (x % i == 0LL) {
            retlist.push_back(i);
            retlist.push_back(x / i);
        }
    }
}

// returns factors and 1
void get_factors(V<ll> &retlist, ll x)
{
    retlist.pb(1LL);
    for (ll i = 2LL; i < (ll)(sqrt(x)) + 3LL; ++i) {
        while (x % i == 0LL) {
            retlist.pb(i);
            x /= i;
        }
    }
    retlist.pb(x);
}

bool is_prime(ll x)
{
    V<ll> factors, factors2;

    get_factors(factors, x);

    for (auto factor : factors) {
        if (factor > 1) factors2.pb(factor);
    }

    return factors2.size() == 1 && x == factors2[0];
}

template <typename T>
void intersection(const set<T> &a, const set<T> &b,
                  set<T> &result)
{
    set_intersection(ALL(a), ALL(b), inserter(result, result.end()));
}

ull combination(ll x, ll y)
{
    if (y > x / 2LL) y = x - y;

    ull ret = 1LL;
    for (ll i = 0LL; i < y; ++i) {
        ret *= x--;
        ret /= (i + 1LL);
    }

    return ret;
}

ull mod_combination(ll x, ll y, ll mod)
{
    if (y > x / 2LL) y = x - y;

    ll ret = 1;

    for (ll i = 0LL; i < y; ++i) {
        ret = (ret * x--) % mod;
        ret = (ret * mod_inv(i + 1LL, mod)) % mod;
    }

    return ret;
}

void make_perms(ll perms[], ll perm_invs[], ll size, ll mod)
{
    perms[0] = 1LL;
    srep (i, 1, size) {
        perms[i] = perms[i-1] * i;
        perms[i] %= mod;
   }

    rep (i, size) {
        perm_invs[i] = mod_inv(perms[i], mod);
    }
}

void make_linklist(const V<t2> &srclist, V<ll> dstlist[])
{
    for (auto src : srclist) {
        ll a = get<0>(src);
        ll b = get<1>(src);
        dstlist[a].pb(b);
        dstlist[b].pb(a);
    }
}

void make_parental_relation(const V<ll> linklist[], ll root, ll n,
                            ll parent[], V<ll> children[], ll level[])
{
    queue<ll> q;
    bool checked[n+1];

    memset(checked, 0, sizeof(checked));

    q.push(root);
    checked[root] = true;
    parent[root] = root;
    level[root] = 0LL;

    for ( ; !(q.empty()); ) {
        ll now = q.front(); q.pop();
        for (auto next : linklist[now]) {
            if (checked[next]) continue;
            q.push(next);
            checked[next] = true;
            parent[next] = now;
            children[now].pb(next);
            level[next] = level[now] + 1LL;
        }
    }
}

void make_subtree_sizes(const ll child_count[], const ll parents[],
                        ll subtree_sizes[], ll n)
{
    ll remain_count[n+1LL];
    memcpy(remain_count, child_count, sizeof(remain_count));

    queue<ll> q;
    srep (node, 1LL, n+1LL) {
        subtree_sizes[node] = 1LL;
        if (remain_count[node] > 0) continue;
        q.push(node);
    }

    while (!q.empty()) {
        ll node = q.front(); q.pop();
        ll parent = parents[node];
        if (node == parent) continue;
        remain_count[parent]--;
        subtree_sizes[parent] += subtree_sizes[node];
        if (remain_count[parent] == 0LL) q.push(parent);
    }
}

void get_centroids(const V<ll> children[], const ll subtree_sizes[],
                   ll root, ll n, V<ll> &centroids)
{
    queue<ll> q;
    q.push(root);

    while (!q.empty()) {
        ll now = q.front(); q.pop();
        bool is_centroid = true;
        for (auto child : children[now]) {
            q.push(child);
            if (subtree_sizes[child] > n / 2LL) is_centroid = false;
        }
        if (n - subtree_sizes[now] > n / 2LL) is_centroid = false;
        if (is_centroid) centroids.pb(now);
    }

    assert(centroids.size() == 1LL || centroids.size() == 2LL);
}

#define POW_ANCESTOR_MAXSIZE   20

// preprocess for get_common_ancestor()
void make_pow_ancestor(const ll parent[], ll n,
                       ll (*pow_ancestor)[POW_ANCESTOR_MAXSIZE])
{
    rep (i, n) pow_ancestor[i+1][0] = parent[i+1];

    for (int pow2 = 1; pow(2, pow2) <= n; ++pow2) {
        rep (i0, n) {
            int i = i0+1;
            ll prev = pow_ancestor[i][pow2-1];
            pow_ancestor[i][pow2] = pow_ancestor[prev][pow2-1];
        }
    }
}

ll get_common_ancestor(ll n, ll x, ll y,
                       const ll (*pow_ancestor)[POW_ANCESTOR_MAXSIZE],
                       const ll level[])
{
    if (level[x] < level[y]) {
        ll diff = level[y] - level[x];
        for ( ; diff; ) {
            ll bit = diff & -diff;
            y = pow_ancestor[y][(int)log2(bit)];
            diff -= bit;
        }
    }
    else {
        ll diff = level[x] - level[y];
        for ( ; diff; ) {
            ll bit = diff & -diff;
            x = pow_ancestor[x][(int)log2(bit)];
            diff -= bit;
        }
    }

    if (x == y) return x;

    rrep (i, (int)log2(n)+1) {
        if (pow_ancestor[x][i] != pow_ancestor[y][i]) {
            x = pow_ancestor[x][i];
            y = pow_ancestor[y][i];
        }
    }

    return pow_ancestor[x][0];
}

void kmp_init(const string &pattern, ll kmp_next[])
{
    kmp_next[0] = -1LL;

    ll plen = pattern.size();
    ll prefix_end = -1;

    rep (suffix_end, pattern.size()) {
        while (prefix_end >= 0 && pattern[suffix_end] != pattern[prefix_end]) {
            prefix_end = kmp_next[prefix_end];
        }
        kmp_next[suffix_end+1] = ++prefix_end;
    }

    kmp_next[0] = 0LL;
}

// founds ... list of text's idx of match position. start position idx.
void kmp_search(const string &text, const string &pattern, const ll kmp_next[],
                V<ll> &founds)
{
    ll text_size = text.size();
    ll pattern_size = pattern.size();
    ll text_start = 0LL;
    ll pattern_idx = 0LL;

    assert(pattern_size <= text_size);

    for ( ; ; ) {
        if (text_start + pattern_idx >= text_size) break;
        if (pattern_idx >= pattern_size) break;

        if (text[text_start+pattern_idx] == pattern[pattern_idx]) {
            pattern_idx++;
            if (pattern_idx == pattern_size) {
                founds.pb(text_start);
                pattern_idx = kmp_next[pattern_idx];
                text_start += (pattern_size - pattern_idx);
            }
        }

        else {
            text_start += (pattern_idx - kmp_next[pattern_idx]);
            pattern_idx = kmp_next[pattern_idx];
            if (pattern_idx == 0LL && text[text_start] != pattern[0]) {
                text_start++;
            }
        }
    }
}

void z_algorithm(ll matchcounts[], const string &str)
{
    ll n = str.size();
    ll base_idx = 0LL;
    memset(matchcounts, 0, sizeof(ll) * n);

    srep (idx, 1LL, n) {

        ll checked_len = base_idx + matchcounts[base_idx];

        if (idx + matchcounts[idx-base_idx] < checked_len) {
            matchcounts[idx] = matchcounts[idx-base_idx];
            continue;
        }

        ll start = max(0LL, base_idx + matchcounts[base_idx] - idx);
        matchcounts[idx] = start;
        srep (cmp, start, n-idx) {
            if (str[cmp] == str[idx+cmp]) matchcounts[idx]++;
            else break;
        }
        base_idx = idx;

    }

    matchcounts[0] = n;
}

void _debug_print(auto x)
{
    cout << x << endl;
}

void _debug_print(const t2 &x)
{
    ll x1 = get<0>(x);
    ll x2 = get<1>(x);
    cout << "-- " << x1 << " -- " << x2 << endl;
}

void _debug_print(const t3 &x)
{
    ll x1 = get<0>(x);
    ll x2 = get<1>(x);
    ll x3 = get<2>(x);
    cout << "-- " << x1 << " -- " << x2 << " -- " << x3 << endl;
}

void _debug_print(const t4 &x)
{
    ll x1 = get<0>(x);
    ll x2 = get<1>(x);
    ll x3 = get<2>(x);
    ll x4 = get<3>(x);
    cout << "-- " << x1 << " -- " << x2
        << " -- " << x3 << " -- " << x4 << endl;
}

template <typename T>
void _debug_print(T xarray[], ll n)
{
    rep (i, n) _debug_print(xarray[i]);
}

template <typename T>
void _debug_print(const V<T> &xlist)
{
    for (auto x : xlist) {
        cout << "-- ";
        _debug_print(x);
    }
}

template <typename T>
void _debug_print(const set<T> &xset)
{
    for (auto x : xset) {
        cout << "-- ";
        _debug_print(x);
    }
}

template <typename TT, typename T>
void _debug_print(const M<TT, T> &xlist)
{
    for (auto x : xlist) {
        TT k = x.first;
        T v = x.second;
        cout << "====" << endl;
        cout << "K=";
        _debug_print(k);
        cout << "V=";
        _debug_print(v);
    }
}

void _debug_print_time(const char *prefix)
{
    struct timeval tv;
    gettimeofday(&tv, NULL);
    struct tm *tm = localtime(&tv.tv_sec);
    printf("-- %s %02d:%02d:%02d.%06ld\n",
           prefix, tm->tm_hour, tm->tm_min, tm->tm_sec, tv.tv_usec);
}

///////////////////////////////////////////////////////////////////////////////

void _main();
int main()
{
    cout << setprecision(12);
    _main();
    return 0;
}

void _main()
{
    ll n; llin(n);
    ll xinit; llin(xinit);
    ll yinit; llin(yinit);
    V<ll> alist; llina(alist, n);

    if (n == 1) {
        cout << abs(yinit - alist[0]) << endl;
        return;
    }

    cout << max(abs(alist[n-1] - alist[n-2]), abs(yinit - alist[n-1])) << endl;
}

///////////////////////////////////////////////////////////////////////////////