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#include "alg/acted_monoid/minidx_add.hpp"
#include "alg/monoid/add.hpp"
#include "alg/monoid/min_idx.hpp"
template <typename E, bool tie_is_left = true>
struct ActedMonoid_MinIdx_Add {
using Monoid_X = Monoid_Min_Idx<E, tie_is_left>;
using Monoid_A = Monoid_Add<E>;
using X = typename Monoid_X::value_type;
using A = typename Monoid_A::value_type;
static constexpr X act(const X &x, const A &a, const ll &size) {
if (x.fi == infty<E>) return x;
return {x.fi + a, x.se};
}
};
#line 2 "alg/monoid/add.hpp"
template <typename E>
struct Monoid_Add {
using X = E;
using value_type = X;
static constexpr X op(const X &x, const X &y) noexcept { return x + y; }
static constexpr X inverse(const X &x) noexcept { return -x; }
static constexpr X power(const X &x, ll n) noexcept { return X(n) * x; }
static constexpr X unit() { return X(0); }
static constexpr bool commute = true;
};
#line 2 "alg/monoid/min_idx.hpp"
template <typename T, bool tie_is_left = true>
struct Monoid_Min_Idx {
using value_type = pair<T, int>;
using X = value_type;
static constexpr bool is_small(const X& x, const X& y) {
if (x.fi < y.fi) return true;
if (x.fi > y.fi) return false;
return (tie_is_left ? (x.se < y.se) : (x.se >= y.se));
}
static X op(X x, X y) { return (is_small(x, y) ? x : y); }
static constexpr X unit() { return {infty<T>, -1}; }
static constexpr bool commute = true;
};
#line 3 "alg/acted_monoid/minidx_add.hpp"
template <typename E, bool tie_is_left = true>
struct ActedMonoid_MinIdx_Add {
using Monoid_X = Monoid_Min_Idx<E, tie_is_left>;
using Monoid_A = Monoid_Add<E>;
using X = typename Monoid_X::value_type;
using A = typename Monoid_A::value_type;
static constexpr X act(const X &x, const A &a, const ll &size) {
if (x.fi == infty<E>) return x;
return {x.fi + a, x.se};
}
};