// need #include #include // data structure #include #include #include #include #include #include #include #include //#include //#include //#include //#include #include // stream //#include //#include //#include #include // etc #include #include #include #include #include #include #include // input #define INIT std::ios::sync_with_stdio(false);std::cin.tie(0); #define VAR(type, ...)type __VA_ARGS__;MACRO_VAR_Scan(__VA_ARGS__); template void MACRO_VAR_Scan(T& t) { std::cin >> t; } templatevoid MACRO_VAR_Scan(First& first, Rest&...rest) { std::cin >> first; MACRO_VAR_Scan(rest...); } #define VEC_ROW(type, n, ...)std::vector __VA_ARGS__;MACRO_VEC_ROW_Init(n, __VA_ARGS__); for(int i=0; i void MACRO_VEC_ROW_Init(int n, T& t) { t.resize(n); } templatevoid MACRO_VEC_ROW_Init(int n, First& first, Rest&...rest) { first.resize(n); MACRO_VEC_ROW_Init(n, rest...); } template void MACRO_VEC_ROW_Scan(int p, T& t) { std::cin >> t[p]; } templatevoid MACRO_VEC_ROW_Scan(int p, First& first, Rest&...rest) { std::cin >> first[p]; MACRO_VEC_ROW_Scan(p, rest...); } #define VEC(type, c, n) std::vector c(n);for(auto& i:c)std::cin>>i; #define MAT(type, c, m, n) std::vector> c(m, std::vector(n));for(auto& r:c)for(auto& i:r)std::cin>>i; // output #define OUT(d) std::cout<=(a);--i) #define REP(i, n) for(int i=0;i=0;--i) #define FORLL(i, a, b) for(ll i=ll(a);i=ll(a);--i) #define REPLL(i, n) for(ll i=0;i=0;--i) #define IN(a, x, b) (a<=x && x inline T CHMAX(T& a, const T b) { return a = (a < b) ? b : a; } template inline T CHMIN(T& a, const T b) { return a = (a > b) ? b : a; } #define EXCEPTION(msg) throw std::string("Exception : " msg " [ in ") + __func__ + " : " + std::to_string(__LINE__) + " lines ]" #define TRY(cond, msg) try {if (cond) EXCEPTION(msg);}catch (std::string s) {std::cerr << s << std::endl;} void CHECKTIME(std::function f) { auto start = std::chrono::system_clock::now(); f(); auto end = std::chrono::system_clock::now(); auto res = std::chrono::duration_cast((end - start)).count(); std::cerr << "[Time:" << res << "ns (" << res / (1.0e9) << "s)]\n"; } // test template std::vector> VV(int n) { return std::vector>(n); } template std::vector> VV(int n, int m, T init = T()) { return std::vector>(n, std::vector(m, init)); } template std::ostream& operator<<(std::ostream& os, std::pair p) { os << "(" << p.first << ", " << p.second << ")"; return os; } // type/const #define int ll using ll = long long; using ull = unsigned long long; using ld = long double; using PAIR = std::pair; using PAIRLL = std::pair; constexpr int INFINT = 1 << 30; // 1.07x10^ 9 constexpr int INFINT_LIM = (1LL << 31) - 1; // 2.15x10^ 9 constexpr ll INFLL = 1LL << 60; // 1.15x10^18 constexpr ll INFLL_LIM = (1LL << 62) - 1 + (1LL << 62); // 9.22x10^18 constexpr double EPS = 1e-9; constexpr int MOD = 1000000007; constexpr double PI = 3.141592653589793238462643383279; namespace oldalgo { int calcParallelogram(int w, int h) { return w * h % MOD; } int calcParallelogramEX(int w, int h) { return w * h * (w + h) / 2 % MOD; } int extra(const std::vector& a) { // O(n^2) yet int n = a.size(); int res = 0; int max = 0, max_i = 0; auto ml(a); auto mr(a); REP(i, n - 1) CHMAX(ml[i + 1], ml[i]); RREP(i, n - 1) CHMAX(mr[i], mr[i + 1]); std::reverse(ALL(mr)); REP(i, n) { if (max < a[i]) { max = a[i]; max_i = i; } } REP(i, n) { ml[i] = max - ml[i]; mr[i] = max - mr[i]; } REP(i, max_i) REP(j, n - max_i - 1) { res += std::min(i, j + 1) * std::min(ml[i], mr[j]); } return res; } int calc(const std::vector& a) { int n = a.size(); int res = 0; std::map> map; int max = 0; REP(i, n) { map[a[i]].emplace_back(i); CHMAX(max, a[i]); } REP(i, n + 1) { // top parallelogram (res += max * calcParallelogram(i, (i - 1) * i / 2 % MOD)) %= MOD; } std::set set; set.insert(PAIR(INFINT, INFINT)); set.insert(PAIR(0, n)); for (auto mit = map.rbegin(); mit != map.rend(); ++mit) { const int& x = mit->first; const auto& v(mit->second); for (auto& vi : v) { auto it = std::prev(set.lower_bound(PAIR(vi, INFINT))); int tl = it->first, tr = it->second; (res += x * calcParallelogramEX(vi - tl + 1, tr - vi)) %= MOD; set.erase(it); if (tl < vi) set.insert(PAIR(tl, vi)); if (vi + 1 < tr) set.insert(PAIR(vi + 1, tr)); } } res -= extra(a); res %= MOD; if (res < 0) res += MOD; return res; } }; namespace newalgo { int calcParallelogram(int w, int h) { return w * h % MOD; } int calcParallelogramEX(int w, int h) { return w * h * (w + h) / 2 % MOD; } int extra(const std::vector& a) { // O(nlogn) int n = a.size(); int res = 0; int max = 0, max_i = 0; auto ml(a), mr(a); REP(i, n - 1) CHMAX(ml[i + 1], ml[i]); RREP(i, n - 1) CHMAX(mr[i], mr[i + 1]); std::reverse(ALL(mr)); REP(i, n) { if (max < a[i]) { max = a[i]; max_i = i; } } REP(i, n) { ml[i] = max - ml[i]; mr[i] = max - mr[i]; } auto cl(ml), cr(mr); RREP(i, n - 1) { (cl[i] += cl[i + 1]) %= MOD; (cr[i] += cr[i + 1]) %= MOD; } int I = max_i, J = n - max_i - 1; FOR(i, 1, std::min(I, J + 1)) { int sum = 0; { // row int p = -1; [&] { // get position p int l = i - 1, r = J - 1; if (ml[i] >= mr[l]) return; if (ml[i] <= mr[r]) { p = J - 1; return; } while (l + 1 < r) { int m = (l + r) / 2; if (ml[i] > mr[m]) r = m; else l = m; } while (ml[i] > mr[r]) --r; p = r; }(); if (p == -1) { (sum += cr[i - 1]) %= MOD; } else { (sum += ml[i] * (p + 2 - i) + cr[p + 1]) %= MOD; } } { // col int p = -1; [&] { // get position p int l = i, r = I - 1; if (mr[i - 1] >= ml[l]) return; if (mr[i - 1] <= ml[r]) { p = I - 1; return; } while (l + 1 < r) { int m = (l + r) / 2; if (mr[i - 1] > ml[m]) r = m; else l = m; } while (mr[i - 1] > ml[r]) --r; p = r; }(); if (p == -1) { (sum += cl[i]) %= MOD; } else { (sum += mr[i - 1] * (p + 1 - i) + cl[p + 1]) %= MOD; } } { // cross sum -= std::min(ml[i], mr[i - 1]); } { // norm sum %= MOD; if (sum < 0) sum += MOD; } { // add (res += sum * i % MOD) %= MOD; } } return res; } int calc(const std::vector& a) { int n = a.size(); int res = 0; std::map> map; int max = 0; REP(i, n) { map[a[i]].emplace_back(i); CHMAX(max, a[i]); } REP(i, n + 1) { // top parallelogram (res += max * calcParallelogram(i, (i - 1) * i / 2 % MOD)) %= MOD; } std::set set; set.insert(PAIR(INFINT, INFINT)); set.insert(PAIR(0, n)); for (auto mit = map.rbegin(); mit != map.rend(); ++mit) { const int& x = mit->first; const auto& v(mit->second); for (auto& vi : v) { auto it = std::prev(set.lower_bound(PAIR(vi, INFINT))); int tl = it->first, tr = it->second; (res += x * calcParallelogramEX(vi - tl + 1, tr - vi)) %= MOD; set.erase(it); if (tl < vi) set.insert(PAIR(tl, vi)); if (vi + 1 < tr) set.insert(PAIR(vi + 1, tr)); } } res -= extra(a); res %= MOD; if (res < 0) res += MOD; return res; } }; signed main() { INIT; VAR(int, n); VEC(int, a, n); if (0) { std::iota(ALL(a), 1); do { int oans = oldalgo::calc(a); int nans = newalgo::calc(a); if (oans != nans) { SHOWVECTOR(a); SHOW(oans); SHOW(nans); VAR(int, x); } } while (std::next_permutation(ALL(a))); } else { OUT(newalgo::calc(a))BR; } return 0; }