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vector<ll> xs; // IMPORTANT: Initialize before constructing Lichao!
int findX(int i) {return distance(xs.begin(), lower_bound(all(xs), i));}
struct Fun{ // Default: Linear function. Change it to needed function type.
ll m, c;
ll operator()(int x) {return m*xs[x] + c;}
};
// Default: Computes min. Change lines with comment for max.
struct Lichao{
static constexpr Fun id = {0, inf}; // {0, -inf}
int n, cap;
vector<Fun> seg;
Lichao() : n(sz(xs)), cap(2<<__lg(n)), seg(2*cap, id) {}
void _insert(Fun f, int l, int r, int i) {
while (i < 2*cap){
int m = (l+r)/2;
if (m >= n) {r = m; i = 2*i; continue;}
Fun &g = seg[i];
if (f(m) < g(m)) swap(f, g); // >
if (f(l) < g(l)) r = m, i = 2*i; // >
else l = m, i = 2*i+1;
}}
void insert(Fun f) {_insert(f, 0, cap, 1);}
void _segmentInsert(Fun f, int l, int r, int a, int b, int i) {
if (l <= a && b <= r) _insert(f, a, b, i);
else if (a < r && l < b){
int m = (a+b)/2;
_segmentInsert(f, l, r, a, m, 2*i);
_segmentInsert(f, l, r, m, b, 2*i+1);
}}
void segmentInsert(Fun f, ll l, ll r) {
_segmentInsert(f, findX(l), findX(r), 0, cap, 1);
}
ll _query(int x) {
ll ans = inf; // -inf
for (int i = x + cap; i > 0; i /= 2) ans = min(ans, seg[i](x)); // max
return ans;
}
ll query(ll x) {return _query(findX(x));}
};
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