// >>> TEMPLATES #include using namespace std; using ll = long long; using ld = long double; using i32 = int32_t; using i64 = int64_t; using u32 = uint32_t; using u64 = uint64_t; #define int ll #define rep(i, n) for (int i = 0; i < (int)(n); i++) #define rep1(i, n) for (int i = 1; i <= (int)(n); i++) #define repR(i, n) for (int i = (int)(n)-1; i >= 0; i--) #define rep1R(i, n) for (int i = (int)(n); i >= 1; i--) #define loop(i, a, B) for (int i = a; i B; i++) #define loopR(i, a, B) for (int i = a; i B; i--) #define all(x) begin(x), end(x) #define allR(x) rbegin(x), rend(x) #define rng(x, l, r) begin(x) + (l), begin(x) + (r) #define pb push_back #define eb emplace_back #define fst first #define snd second template auto mp(A &&a, B &&b) { return make_pair(forward(a), forward(b)); } template auto mt(T&&... x) { return make_tuple(forward(x)...); } template auto constexpr inf_ = numeric_limits::max()/2-1; auto constexpr INF32 = inf_; auto constexpr INF64 = inf_; auto constexpr INF = inf_; #ifdef LOCAL #include "debug.hpp" #else #define dump(...) (void)(0) #define say(x) (void)(0) #define debug if (0) #endif template struct pque : priority_queue, Comp> { vector &data() { return this->c; } void clear() { this->c.clear(); } }; template using pque_max = pque>; template using pque_min = pque>; template ::value, int> = 0> ostream& operator<<(ostream& os, T const& a) { bool f = true; for (auto const& x : a) os << (f ? "" : " ") << x, f = false; return os; } template ::value, int> = 0> ostream& operator<<(ostream& os, const T (&a)[N]) { bool f = true; for (auto const& x : a) os << (f ? "" : " ") << x, f = false; return os; } template ())), class = typename enable_if::value>::type> istream& operator>>(istream& is, T &a) { for (auto& x : a) is >> x; return is; } template ostream& operator<<(ostream& os, pair const& p) { return os << p.first << " " << p.second; } template istream& operator>>(istream& is, pair& p) { return is >> p.first >> p.second; } struct IOSetup { IOSetup() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(15); } } iosetup; template struct FixPoint : private F { constexpr FixPoint(F&& f) : F(forward(f)) {} template constexpr auto operator()(T&&... x) const { return F::operator()(*this, forward(x)...); } }; struct MakeFixPoint { template constexpr auto operator|(F&& f) const { return FixPoint(forward(f)); } }; #define MFP MakeFixPoint()| #define def(name, ...) auto name = MFP [&](auto &&name, __VA_ARGS__) template struct vec_impl { using type = vector::type>; template static type make_v(size_t n, U&&... x) { return type(n, vec_impl::make_v(forward(x)...)); } }; template struct vec_impl { using type = T; static type make_v(T const& x = {}) { return x; } }; template using vec = typename vec_impl::type; template auto make_v(Args&&... args) { return vec_impl::make_v(forward(args)...); } template void quit(T const& x) { cout << x << endl; exit(0); } template constexpr bool chmin(T& x, U const& y) { if (x > y) { x = y; return true; } return false; } template constexpr bool chmax(T& x, U const& y) { if (x < y) { x = y; return true; } return false; } template constexpr auto sumof(It b, It e) { return accumulate(b, e, typename iterator_traits::value_type{}); } template int sz(T const& x) { return x.size(); } template int lbd(C const& v, T const& x) { return lower_bound(begin(v), end(v), x)-begin(v); } template int ubd(C const& v, T const& x) { return upper_bound(begin(v), end(v), x)-begin(v); } const int dx[] = { 1, 0, -1, 0, 1, -1, -1, 1 }; const int dy[] = { 0, 1, 0, -1, 1, 1, -1, -1 }; constexpr int popcnt(ll x) { return __builtin_popcountll(x); } template pair operator+(pair const& p, pair const& q) { return { p.first + q.first, p.second + q.second }; } template pair operator-(pair const& p, pair const& q) { return { p.first - q.first, p.second - q.second }; } mt19937_64 seed_{random_device{}()}; template Int rand(Int a, Int b) { return uniform_int_distribution(a, b)(seed_); } i64 irand(i64 a, i64 b) { return rand(a, b); } // [a, b] u64 urand(u64 a, u64 b) { return rand(a, b); } // template void shuffle(It l, It r) { shuffle(l, r, seed_); } // <<< // >>> BIT 2D template struct BIT2D { vector> pos; vector xs, ys; vector bit; vector idx; bool built = false; BIT2D() {} void add_point(Int x, Int y) { pos.emplace_back(x, y); built = false; } void build() { auto make_unique = [&](auto &v) { v.resize(unique(v.begin(), v.end())-v.begin()); }; sort(pos.begin(), pos.end()); make_unique(pos); for (auto [x, y] : pos) xs.push_back(x); make_unique(xs); int n = xs.size(); idx.resize(n+1); vector> z(n); int i = 0; for (auto [x, y] : pos) { if (xs[i] < x) i++; z[i].push_back(y); } for (i = 0; i < n; i++) { make_unique(z[i]); int j = i | (i + 1); if (j >= n) continue; int A = z[j].size(), B = z[i].size(); z[j].reserve(A + B); copy(z[i].begin(), z[i].end(), back_inserter(z[j])); inplace_merge(z[j].begin(), z[j].begin() + A, z[j].end()); } for (i = 0; i < n; i++) { copy(z[i].begin(), z[i].end(), back_inserter(ys)); idx[i+1] = ys.size(); } bit.resize(idx.back()); built = true; } void add(Int x, Int y, T const& val) { assert(built); int i = lower_bound(xs.begin(), xs.end(), x) - xs.begin(); assert(i < (int)xs.size() and xs[i] == x); for ( ; i < (int)xs.size(); i |= i + 1) { auto it = lower_bound(ys.begin() + idx[i], ys.begin() + idx[i+1], y); assert(it != ys.end() and *it == y); int j = it - (ys.begin() + idx[i]); for ( ; idx[i] + j < idx[i+1]; j |= j + 1) { bit[idx[i] + j] += val; } } } T sum(Int xr, Int yl, Int yr) const { assert(built); int i = lower_bound(xs.begin(), xs.end(), xr) - xs.begin(); T s = 0; for (i-- ; i >= 0; i = (i & (i + 1)) - 1) { int j = lower_bound(ys.begin() + idx[i], ys.begin() + idx[i+1], yr) - (ys.begin() + idx[i]); for (j-- ; j >= 0; j = (j & (j + 1)) - 1) { s += bit[idx[i] + j]; } j = lower_bound(ys.begin() + idx[i], ys.begin() + idx[i+1], yl) - (ys.begin() + idx[i]); for (j-- ; j >= 0; j = (j & (j + 1)) - 1) { s -= bit[idx[i] + j]; } } return s; } T sum(Int xl, Int xr, Int yl, Int yr) const { return sum(xr, yl, yr) - sum(xl, yl, yr); } T get(Int x, Int y) const { return sum(x, x+1, y, y+1); } vector dat() const { assert(built); vector ret; for (auto [x, y] : pos) ret.push_back(get(x, y)); return ret; } }; // <<< // >>> BIT struct BIT { int n; vector v; // use v[1..n] BIT(int n = 0) : n(n), v(n+1) {} int size() const { return n; } int operator[](int i) const { return get(i); } int get(int i) const { return sum(i+1)-sum(i); } void set(int i, int x) { add(i, x-get(i)); } void add(int i, int x) { assert(0 <= i); assert(i < n); for (i++; i <= n; i += i&(-i)) v[i] += x; } int sum(int r) const { // [0, r) assert(0 <= r); assert(r <= n); int s = 0; for (int i = r; i > 0; i -= i&(-i)) s += v[i]; return s; } int sum(int l, int r) const { // [l, r) return sum(r)-sum(l); } // lower_bound({sum(0), sum(1), ..., sum(n)}, x) int lower_bound(int x) const { if (x <= 0) return 0; int s = 0, i = 0, w = 1; while (2*w <= n) w *= 2; for ( ; w; w >>= 1) { if (i+w <= n && s+v[i+w] < x) { s += v[i+w]; i += w; } } return i+1; } int upper_bound(int x) const { if (x < 0) return 0; int s = 0, i = 0, w = 1; while (2*w <= n) w *= 2; for ( ; w; w >>= 1) { if (i+w <= n && s+v[i+w] <= x) { s += v[i+w]; i += w; } } return i+1; } }; // <<< int32_t main() { int n; cin >> n; vector a(n); rep (i, n) cin >> a[i], --a[i]; if (a[0] > a[1]) rep (i, n) a[i] = n-1-a[i]; vector> p[2]; rep (i, n) { if (i % 2 == 0) { int L = i-1 >= 0 ? a[i-1] : INF; int R = i+1 < n ? a[i+1] : INF; assert(a[i] <= min(L, R)-1); p[0].eb(a[i], min(L, R)-1); } else { int L = i-1 >= 0 ? a[i-1] : -INF; int R = i+1 < n ? a[i+1] : -INF; assert(a[i] >= max(L, R) + 1); p[1].eb(a[i], max(L, R) + 1); } } int ans = 0; { BIT bit(n); sort(all(p[0])); for (auto [x, y] : p[0]) { ans += bit.sum(x, n); bit.add(y, +1); } } dump(ans); { BIT bit(n); sort(all(p[1])); for (auto [x, y] : p[1]) { ans += bit.sum(y, n); bit.add(x, +1); } } dump(ans); vector> es; for (auto [x, y] : p[1]) es.eb(x, -1, y); for (auto [x, y] : p[0]) es.eb(y, +1, x); sort(all(es)); BIT bit(n+1); for (auto [x, t, y] : es) { if (t < 0) { bit.add(y, +1); } else { ans += bit.sum(0, y+1); } } cout << ans << "\n"; }