Problem: Write a program which manipulates a sequence $A$ = {$a_0, a_1, ..., a_{n-1}$} with the following operations:

* $add(s, t, x)$ : add $x$ to $a_s, a_{s+1}, ..., a_t$.
* $find(s, t)$ : report the minimum value in $a_s, a_{s+1}, ..., a_t$.



Note that the initial values of $a_i ( i = 0, 1, ..., n-1 )$ are 0.

Constraints

* $1 ≤ n ≤ 100000$
* $1 ≤ q ≤ 100000$
* $0 ≤ s ≤ t < n$
* $-1000 ≤ x ≤ 1000$

Input


$n$ $q$
$query_1$
$query_2$
:
$query_q$


In the first line, $n$ (the number of elements in $A$) and $q$ (the number of queries) are given. Then, $i$th query $query_i$ is given in the following format:


0 $s$ $t$ $x$


or


1 $s$ $t$


The first digit represents the type of the query. '0' denotes $add(s, t, x)$ and '1' denotes $find(s, t)$.

Output

For each $find$ query, print the minimum value.

Example

Input

6 7
0 1 3 1
0 2 4 -2
1 0 5
1 0 1
0 3 5 3
1 3 4
1 0 5


Output

-2
0
1
-1

Solution (in CPP):

Solution:
#include <algorithm>
#include <iostream>
#include <vector>
#include <functional>
using namespace std;

template<typename Monoid, typename OperatorMonoid>
struct LazySegmentTree {
    using F = function<Monoid(Monoid, Monoid)>;
    using G = function<Monoid(Monoid, OperatorMonoid)>;
    using H = function<OperatorMonoid(OperatorMonoid, OperatorMonoid)>;
    const F f;
    const G g;
    const H h;
    const Monoid M1;
    const OperatorMonoid OM0;
    int sz, height;
    vector<Monoid> data;
    vector<OperatorMonoid> lazy;
    LazySegmentTree(int n, const F f, const G g, const H h,
                    const Monoid &M1, const OperatorMonoid &OM0)
        : f(f), g(g), h(h), M1(M1), OM0(OM0), sz(1), height(0)
    {
        while (sz < n) sz <<= 1, height++;
        data.assign(sz * 2, M1);
        lazy.assign(sz * 2, OM0);
    }
    void set(int k, const Monoid &x) { data[k + sz] = x; }
    void build() {
        for (int k = sz - 1; k > 0; k--) {
            data[k] = f(data[k << 1 | 0], data[k << 1 | 1]);
        }
    }
    inline Monoid reflect(int k) {
        return lazy[k] == OM0 ? data[k] : g(data[k], lazy[k]);
    }
    inline void propagate(int k) {
        if (lazy[k] == OM0) return ;
        lazy[k << 1 | 0] = h(lazy[k << 1 | 0], lazy[k]);
        lazy[k << 1 | 1] = h(lazy[k << 1 | 1], lazy[k]);
        data[k] = reflect(k);
        lazy[k] = OM0;
    }
    inline void thrust(int k) {
        for (int i = height; i > 0; i--) propagate(k >> i);
    }
    inline void recalc(int k) {
        while (k >>= 1) data[k] = f(reflect(k << 1 | 0), reflect(k << 1 | 1));
    }
    void update(int a, int b, const OperatorMonoid &x) {
        thrust(a += sz);
        thrust(b += sz - 1);
        for (int l = a, r = b + 1; l < r; l >>= 1, r >>= 1) {
            if (l & 1) lazy[l] = h(lazy[l], x), ++l;
            if (r & 1) --r, lazy[r] = h(lazy[r], x);
        }
        recalc(a);
        recalc(b);
    }
    Monoid get(int a, int b) {
        thrust(a += sz);
        thrust(b += sz - 1);
        Monoid L = M1, R = M1;
        for (int l = a, r = b + 1; l < r; l >>= 1, r >>= 1) {
            if (l & 1) L = f(L, reflect(l++));
            if (r & 1) R = f(reflect(--r), R);
        }
        return f(L, R);
    }
    Monoid operator[](const int &k) { return get(k, k + 1); }
};

const int MAX = numeric_limits<int>::max();
int main() {
    int n, q; cin >> n >> q;
    using T = int;
    using E = int;
    auto f = [](T a, T b) { return T(min(a, b)); };
    auto g = [](T a, E b) { return T(a + b); };
    auto h = [](E a, E b) { return E(a + b); };
    LazySegmentTree<T, E> seg(n, f, g, h, T(MAX), E(0));
    for (int i = 0; i < n; i++) seg.set(i, 0);
    seg.build();
    while (q--) {
        int op; cin >> op;
        int s, t; cin >> s >> t; t++;
        if (op == 0) {
            int x; cin >> x;
            seg.update(s, t, x);
        }
        if (op == 1) {
            cout << seg.get(s, t) << endl;
        }
    }
    return 0;
}