#include using namespace std; //#pragma GCC optimize("Ofast") //#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native") #define ms(s, n) memset(s, n, sizeof(s)) #define FOR(i, a, b) for (int i = (a); i < (b); ++i) #define FORd(i, a, b) for (int i = (a) - 1; i >= (b); --i) #define FORall(it, a) for (__typeof((a).begin()) it = (a).begin(); it != (a).end(); it++) #define sz(a) int((a).size()) #define pconent(t, x) (t.find(x) != t.end()) #define all(a) (a).begin(), (a).end() #define uni(a) (a).erase(unique(all(a)), (a).end()) #define pb push_back #define pf push_front #define mp make_pair #define fi first #define se second #define prec(n) fixed<> (i)) & 1) #define bitcount(n) __builtin_popcountll(n) typedef long long ll; typedef unsigned long long ull; typedef long double ld; typedef pair pi; typedef vector vi; typedef vector vii; const int MOD = (int) 1e9 + 7; const int FFTMOD = 1007681537; const int INF = (int) 1e9; const ll LINF = (ll) 1e18; const ld PI = acos((ld) -1); const ld EPS = 1e-9; inline ll gcd(ll a, ll b) {ll r; while (b) {r = a % b; a = b; b = r;} return a;} inline ll lcm(ll a, ll b) {return a / gcd(a, b) * b;} inline ll fpow(ll n, ll k, int p = MOD) {ll r = 1; for (; k; k >>= 1) {if (k & 1) r = r * n % p; n = n * n % p;} return r;} template inline int chkmin(T& a, const T& val) {return val < a ? a = val, 1 : 0;} template inline int chkmax(T& a, const T& val) {return a < val ? a = val, 1 : 0;} inline ll isqrt(ll k) {ll r = sqrt(k) + 1; while (r * r > k) r--; return r;} inline ll icbrt(ll k) {ll r = cbrt(k) + 1; while (r * r * r > k) r--; return r;} inline void addmod(int& a, int val, int p = MOD) {if ((a = (a + val)) >= p) a -= p;} inline void submod(int& a, int val, int p = MOD) {if ((a = (a - val)) < 0) a += p;} inline int mult(int a, int b, int p = MOD) {return (ll) a * b % p;} inline int inv(int a, int p = MOD) {return fpow(a, p - 2, p);} inline int sign(ld x) {return x < -EPS ? -1 : x > +EPS;} inline int sign(ld x, ld y) {return sign(x - y);} #define db(x) cerr << #x << " = " << (x) << " "; #define endln cerr << "\n"; template struct MINRMQ { int n; vector a; vector > f; T best(T a, T b) { return min(a, b); } void init(int n) { this->n = n; int p = 1; while ((1 << p) < n) p++; a.resize(n), f.resize(p + 1); for (int i = 0; i < (int) f.size(); i++) { f[i].resize(n); } } void upd(int u, T x) { a[u] = x; } void build() { for (int i = 0; i < n; i++) f[0][i] = a[i]; for (int l = 0, k; (k = 1 << l) < n; l++) { for (int i = 0; i + k < n; i++) { f[l + 1][i] = best(f[l][i], f[l][i + k]); } } } T query(int a, int b) { int l = a == b ? 0 : __lg(b - a); return best(f[l][a], f[l][b - (1 << l) + 1]); } }; template struct MAXRMQ { int n; vector a; vector > f; T best(T a, T b) { return max(a, b); } void init(int n) { this->n = n; int p = 1; while ((1 << p) < n) p++; a.resize(n), f.resize(p + 1); for (int i = 0; i < (int) f.size(); i++) { f[i].resize(n); } } void upd(int u, T x) { a[u] = x; } void build() { for (int i = 0; i < n; i++) f[0][i] = a[i]; for (int l = 0, k; (k = 1 << l) < n; l++) { for (int i = 0; i + k < n; i++) { f[l + 1][i] = best(f[l][i], f[l][i + k]); } } } T query(int a, int b) { int l = a == b ? 0 : __lg(b - a); return best(f[l][a], f[l][b - (1 << l) + 1]); } }; template struct GCDRMQ { int n; vector a; vector > f; T best(T a, T b) { return __gcd(abs(a), abs(b)); } void init(int n) { this->n = n; int p = 1; while ((1 << p) < n) p++; a.resize(n), f.resize(p + 1); for (int i = 0; i < (int) f.size(); i++) { f[i].resize(n); } } void upd(int u, T x) { a[u] = x; } void build() { for (int i = 0; i < n; i++) f[0][i] = a[i]; for (int l = 0, k; (k = 1 << l) < n; l++) { for (int i = 0; i + k < n; i++) { f[l + 1][i] = best(f[l][i], f[l][i + k]); } } } T query(int a, int b) { int l = a == b ? 0 : __lg(b - a); return best(f[l][a], f[l][b - (1 << l) + 1]); } }; MINRMQ minrmq; MAXRMQ maxrmq; GCDRMQ gcdrmq; const int maxn = 1e6 + 5; int n; long long a[maxn]; long long b[maxn]; int l[maxn]; int r[maxn]; int getnext(int i, int u, int v) { int g = gcdrmq.query(u, v); int lo = v, hi = r[i]; while (lo < hi) { int mi = lo + hi + 1 >> 1; if (gcdrmq.query(u, mi) == g) { lo = mi; } else { hi = mi - 1; } } return lo + hi >> 1; } int getprev(int i, int u, int v) { int g = gcdrmq.query(u, v); int lo = l[i], hi = u; while (lo < hi) { int mi = lo + hi >> 1; if (gcdrmq.query(mi, v) != g) { lo = mi + 1; } else { hi = mi; } } return lo + hi >> 1; } long long query1(int i, int u, int x, int y) { return gcdrmq.query(u, x) * (maxrmq.query(x, y) - b[u - 1] - a[i]); } long long query2(int i, int x, int y, int u) { return gcdrmq.query(y, u) * (b[u] - minrmq.query(x - 1, y - 1) - a[i]); } long long ff(int i, int u, int v) { return gcdrmq.query(u, v) * (b[v] - b[u - 1] - a[i]); } void solve() { cin >> n; FOR(i, 1, n + 1) cin >> a[i]; partial_sum(a, a + n + 1, b); minrmq.init(n + 1); maxrmq.init(n + 1); gcdrmq.init(n + 1); FOR(i, 1, n + 1) minrmq.upd(i, b[i]); FOR(i, 1, n + 1) maxrmq.upd(i, b[i]); FOR(i, 1, n + 1) gcdrmq.upd(i, a[i]); minrmq.build(); maxrmq.build(); gcdrmq.build(); FOR(i, 1, n + 1) l[i] = r[i] = i; FOR(i, 2, n + 1) { int ptr = i; while (ptr > 1 && a[i] >= a[ptr - 1]) ptr = l[ptr - 1]; l[i] = ptr; } FORd(i, n, 1) { int ptr = i; while (ptr < n && a[i] > a[ptr + 1]) ptr = r[ptr + 1]; r[i] = ptr; } long long res = -8 * LINF; FOR(i, 1, n + 1) { if (i - l[i] < r[i] - i) { FORd(j, i + 1, l[i]) { int ptr = i; while (ptr <= r[i]) { int nptr = getnext(i, j, ptr); chkmax(res, query1(i, j, ptr, nptr)); ptr = nptr + 1; } } } else { FOR(j, i, r[i] + 1) { int ptr = i; while (ptr >= l[i]) { int nptr = getprev(i, ptr, j); chkmax(res, query2(i, nptr, ptr, j)); ptr = nptr - 1; } } } } cout << res << "\n"; } int main(int argc, char* argv[]) { ios_base::sync_with_stdio(0), cin.tie(0); if (argc > 1) { assert(freopen(argv[1], "r", stdin)); } if (argc > 2) { assert(freopen(argv[2], "wb", stdout)); } solve(); cerr << "\nTime elapsed: " << 1000 * clock() / CLOCKS_PER_SEC << "ms\n"; return 0; }