#include using namespace std; template inline void chmax(T& a, const T b){a=max(a,b);} inline void balanceLtoR(multiset& stl,multiset& str) { while(stl.size()>str.size()+1) { long long tmp = *stl.rbegin(); str.insert(tmp); stl.erase(stl.find(tmp)); } } inline void balanceRtoL(multiset& stl,multiset& str) { if(stl.size()& stl,multiset& str){ long long tmpl = *stl.rbegin(); long long tmpr = *str.begin(); if(tmpl>tmpr) { stl.erase(stl.find(tmpl)); stl.insert(tmpr); str.erase(str.find(tmpr)); str.insert(tmpl); } } int main() { cin.tie(0);ios::sync_with_stdio(false); int N; cin >> N; // assert(1<=N && N <= 5000); vector A(N); for(int i = 0; i < N; ++i) cin >> A[i]; // for(int i = 0; i < N; ++i) assert(-1000000000<=A[i] && A[i] <= 1000000000); //クエリ区間を列挙、調和級数なのでO(N*logN) vector> range; for(int n = 1; n <= N; ++n) { int M = N/n; for(int i = 0; i+n <= N; i+=n) range.push_back({i,i+n-1}); for(int i = N-M*n; i+n <= N; i+=n) range.push_back({i,i+n-1}); } //Mo順ソート O(N*logN*log(NlogN)) int bucket = max(1,(int)sqrt(N)-10); vector idx(range.size()); iota(idx.begin(),idx.end(),0); sort(idx.begin(),idx.end(),[&](int a, int b){ auto al = range[a].first/bucket; auto& ar = range[a].second; auto bl = range[b].first/bucket; auto& br = range[b].second; return (al != bl) ? (al < bl) : ((al%2)?(ar > br):(ar < br)); }); //Moで中央値列挙 O(N*sqrt(N)*(logN)^2) int l = 0, r = 0; multiset stl,str; stl.insert(A[0]); unordered_map mp; for(int& i:idx){ auto& xl = range[i].first; auto& xr = range[i].second; if(mp.count(xl*N+xr))continue; //左端を広げる while(xl < l){ l--; stl.insert(A[l]); if(str.size()) exchange(stl,str); balanceLtoR(stl,str); } //右端を広げる while(r < xr){ r++; stl.insert(A[r]); if(str.size()) exchange(stl,str); balanceLtoR(stl,str); } //左端を狭める while(l < xl){ if(stl.count(A[l])) { stl.erase(stl.find(A[l])); balanceRtoL(stl,str); } else { str.erase(str.find(A[l])); balanceLtoR(stl,str); } l++; } //右端を狭める while(xr < r){ if(stl.count(A[r])) { stl.erase(stl.find(A[r])); balanceRtoL(stl,str); } else { str.erase(str.find(A[r])); balanceLtoR(stl,str); } r--; } mp[xl*N+xr] = *stl.rbegin(); } long long ans = 0; int cnt = 0; //区間長決め打ち全探索O(N*logN) for(long long n = 1; n <= N; ++n) { int M = N/n; vector lSum(M,0),rSum(M,0); vector> lRange(M),rRange(M); //区間取得 for(int i = 0; i < M; ++i) { lRange[i] = range[cnt + i]; lSum[i] = n*mp[lRange[i].first*N+lRange[i].second]; rRange[i] = range[cnt + i + M]; rSum[i] = n*mp[rRange[i].first*N+rRange[i].second]; } //累積和 for(int i = 1; i < M; ++i) lSum[i] += lSum[i-1]; for(int i = M-2; 0 <= i; --i) rSum[i] += rSum[i+1]; //累積max for(int i = 1; i < M; ++i) chmax(lSum[i],lSum[i-1]); for(int i = M-2; 0 <= i; --i) chmax(rSum[i],rSum[i+1]); chmax(ans,lSum[M-1]); chmax(ans,rSum[0]); //尺取りしながら左右決め打ち全探索 int j = 0; for(int i = 0; i < M; ++i) { while(j < M && lRange[i].second >= rRange[j].first) j++; if(j