#include #include #include using namespace std; #ifndef ATCODER_INTERNAL_BITOP_HPP #define ATCODER_INTERNAL_BITOP_HPP 1 #ifdef _MSC_VER #include #endif namespace atcoder { namespace internal { // @param n `0 <= n` // @return minimum non-negative `x` s.t. `n <= 2**x` int ceil_pow2(int n) { int x = 0; while ((1U << x) < (unsigned int)(n)) x++; return x; } // @param n `1 <= n` // @return minimum non-negative `x` s.t. `(n & (1 << x)) != 0` int bsf(unsigned int n) { #ifdef _MSC_VER unsigned long index; _BitScanForward(&index, n); return index; #else return __builtin_ctz(n); #endif } } // namespace internal } // namespace atcoder #endif // ATCODER_INTERNAL_BITOP_HPP #ifndef ATCODER_LAZYSEGTREE_HPP #define ATCODER_LAZYSEGTREE_HPP 1 #include #include #include #include // #include "atcoder/internal_bit" namespace atcoder { template struct lazy_segtree { public: lazy_segtree() : lazy_segtree(0) {} explicit lazy_segtree(int n) : lazy_segtree(std::vector(n, e())) {} explicit lazy_segtree(const std::vector& v) : _n(int(v.size())) { log = internal::ceil_pow2(_n); size = 1 << log; d = std::vector(2 * size, e()); lz = std::vector(size, id()); for (int i = 0; i < _n; i++) d[size + i] = v[i]; for (int i = size - 1; i >= 1; i--) { update(i); } } void set(int p, S x) { assert(0 <= p && p < _n); p += size; for (int i = log; i >= 1; i--) push(p >> i); d[p] = x; for (int i = 1; i <= log; i++) update(p >> i); } S get(int p) const { assert(0 <= p && p < _n); p += size; for (int i = log; i >= 1; i--) push(p >> i); return d[p]; } S prod(int l, int r) const { assert(0 <= l && l <= r && r <= _n); if (l == r) return e(); l += size; r += size; for (int i = log; i >= 1; i--) { if (((l >> i) << i) != l) push(l >> i); if (((r >> i) << i) != r) push((r - 1) >> i); } S sml = e(), smr = e(); while (l < r) { if (l & 1) sml = op(sml, d[l++]); if (r & 1) smr = op(d[--r], smr); l >>= 1; r >>= 1; } return op(sml, smr); } S all_prod() const { return d[1]; } void apply(int p, F f) { assert(0 <= p && p < _n); p += size; for (int i = log; i >= 1; i--) push(p >> i); d[p] = mapping(f, d[p]); for (int i = 1; i <= log; i++) update(p >> i); } void apply(int l, int r, F f) { assert(0 <= l && l <= r && r <= _n); if (l == r) return; l += size; r += size; for (int i = log; i >= 1; i--) { if (((l >> i) << i) != l) push(l >> i); if (((r >> i) << i) != r) push((r - 1) >> i); } { int l2 = l, r2 = r; while (l < r) { if (l & 1) all_apply(l++, f); if (r & 1) all_apply(--r, f); l >>= 1; r >>= 1; } l = l2; r = r2; } for (int i = 1; i <= log; i++) { if (((l >> i) << i) != l) update(l >> i); if (((r >> i) << i) != r) update((r - 1) >> i); } } template int max_right(int l) const { return max_right(l, [](S x) { return g(x); }); } template int max_right(int l, G g) const { assert(0 <= l && l <= _n); assert(g(e())); if (l == _n) return _n; l += size; for (int i = log; i >= 1; i--) push(l >> i); S sm = e(); do { while (l % 2 == 0) l >>= 1; if (!g(op(sm, d[l]))) { while (l < size) { push(l); l = (2 * l); if (g(op(sm, d[l]))) { sm = op(sm, d[l]); l++; } } return l - size; } sm = op(sm, d[l]); l++; } while ((l & -l) != l); return _n; } template int min_left(int r) const { return min_left(r, [](S x) { return g(x); }); } template int min_left(int r, G g) const { assert(0 <= r && r <= _n); assert(g(e())); if (r == 0) return 0; r += size; for (int i = log; i >= 1; i--) push((r - 1) >> i); S sm = e(); do { r--; while (r > 1 && (r % 2)) r >>= 1; if (!g(op(d[r], sm))) { while (r < size) { push(r); r = (2 * r + 1); if (g(op(d[r], sm))) { sm = op(d[r], sm); r--; } } return r + 1 - size; } sm = op(d[r], sm); } while ((r & -r) != r); return 0; } protected: int _n, size, log; mutable std::vector d; mutable std::vector lz; void update(int k) const { d[k] = op(d[2 * k], d[2 * k + 1]); } virtual void all_apply(int k, F f) const { d[k] = mapping(f, d[k]); if (k < size) lz[k] = composition(f, lz[k]); } void push(int k) const { all_apply(2 * k, lz[k]); all_apply(2 * k + 1, lz[k]); lz[k] = id(); } }; } // namespace atcoder #endif // ATCODER_LAZYSEGTREE_HPP template class segtree_beats : public atcoder::lazy_segtree { using Base = atcoder::lazy_segtree; using Base::lazy_segtree; void all_apply(int k, F f) const override { Base::d[k] = mapping(f, Base::d[k]); if (k < Base::size) { Base::lz[k] = composition(f, Base::lz[k]); if (Base::d[k].fail) Base::push(k), Base::update(k); } } }; namespace RangeChMinMaxAddSum { #include template inline Num second_lowest(Num a, Num a2, Num c, Num c2) noexcept { // a < a2, c < c2 return a == c ? std::min(a2, c2) : a2 <= c ? a2 : c2 <= a ? c2 : std::max(a, c); } template inline Num second_highest(Num a, Num a2, Num b, Num b2) noexcept { // a > a2, b > b2 return a == b ? std::max(a2, b2) : a2 >= b ? a2 : b2 >= a ? b2 : std::min(a, b); } using BNum = long long; constexpr BNum BINF = 1LL << 61; struct S { BNum lo, hi, lo2, hi2, sum; unsigned sz, nlo, nhi; bool fail; S() : lo(BINF), hi(-BINF), lo2(BINF), hi2(-BINF), sum(0), sz(0), nlo(0), nhi(0), fail(0) {} S(BNum x, unsigned sz_ = 1) : lo(x), hi(x), lo2(BINF), hi2(-BINF), sum(x * sz_), sz(sz_), nlo(sz_), nhi(sz_), fail(0) {} friend std::ostream &operator<<(std::ostream &os, const S s) { return os << "[(" << s.lo << "x" << s.nlo << ", " << s.lo2 << ", " << s.hi2 << ", " << s.hi << "x" << s.nhi << "), sz=" << s.sz << ", sum=" << s.sum << "]"; } }; S e() { return S(); } S op(S l, S r) { if (l.lo > l.hi) return r; if (r.lo > r.hi) return l; S ret; ret.lo = std::min(l.lo, r.lo), ret.hi = std::max(l.hi, r.hi); ret.lo2 = second_lowest(l.lo, l.lo2, r.lo, r.lo2), ret.hi2 = second_highest(l.hi, l.hi2, r.hi, r.hi2); ret.sum = l.sum + r.sum, ret.sz = l.sz + r.sz; ret.nlo = l.nlo * (l.lo <= r.lo) + r.nlo * (r.lo <= l.lo); ret.nhi = l.nhi * (l.hi >= r.hi) + r.nhi * (r.hi >= l.hi); return ret; } struct F { BNum lb, ub, bias; F() : lb(-BINF), ub(BINF), bias(0) {} F(BNum chmax_, BNum chmin_, BNum add) : lb(chmax_), ub(chmin_), bias(add) {} static F chmin(BNum x) noexcept { return F(-BINF, x, BNum(0)); } static F chmax(BNum x) noexcept { return F(x, BINF, BNum(0)); } static F add(BNum x) noexcept { return F(-BINF, BINF, x); }; }; F composition(F fnew, F fold) { F ret; ret.lb = std::max(std::min(fold.lb + fold.bias, fnew.ub), fnew.lb) - fold.bias; ret.ub = std::min(std::max(fold.ub + fold.bias, fnew.lb), fnew.ub) - fold.bias; ret.bias = fold.bias + fnew.bias; return ret; } F id() { return F(); } S mapping(F f, S x) { if (x.sz == 0) return e(); if (x.lo == x.hi or f.lb == f.ub or f.lb >= x.hi or f.ub < x.lo) return S(std::min(std::max(x.lo, f.lb), f.ub) + f.bias, x.sz); if (x.lo2 == x.hi) { x.lo = x.hi2 = std::max(x.lo, f.lb) + f.bias, x.hi = x.lo2 = std::min(x.hi, f.ub) + f.bias; x.sum = x.lo * x.nlo + x.hi * x.nhi; return x; } if (f.lb < x.lo2 and f.ub > x.hi2) { BNum nxt_lo = std::max(x.lo, f.lb), nxt_hi = std::min(x.hi, f.ub); x.sum += (nxt_lo - x.lo) * x.nlo - (x.hi - nxt_hi) * x.nhi + f.bias * x.sz; x.lo = nxt_lo + f.bias, x.hi = nxt_hi + f.bias, x.lo2 += f.bias, x.hi2 += f.bias; return x; } x.fail = 1; return x; } using segtree = segtree_beats; } // namespace RangeChMinMaxAddSum int main() { ios::sync_with_stdio(false), cin.tie(nullptr); int N; cin >> N; vector> v2is(N); for (int i = 0; i < N; i++) { int a; cin >> a; v2is[a - 1].push_back(i); } vector> ranges{{0, N}}; long long ret = 0; vector init; for (int i = 0; i < N; i++) init.emplace_back(i); RangeChMinMaxAddSum::segtree tree(init); for (auto is : v2is) { if (ranges.empty()) break; int l = 0; for (auto i : is) { tree.apply(l, i + 1, RangeChMinMaxAddSum::F::chmax(i)); l = i + 1; } tree.apply(l, N, RangeChMinMaxAddSum::F::chmax(N)); auto tmp = (long long)N * N - tree.all_prod().sum; ret += tmp; if (!tmp) break; } cout << ret + (long long)N * (N + 1) / 2 << '\n'; }