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 <iostream>
#include <algorithm>
#include <iomanip>
#include <map>
#include <set>
#include <queue>
#include <stack>
#include <numeric>
#include <bitset>
#include <cmath>

static const int MOD = 1000000007;
using ll = long long;
using u32 = uint32_t;
using namespace std;

template<class T> constexpr T INF = ::numeric_limits<T>::max()/32*15+208;

template <class M>
struct LazySegmentTree{
    using T = typename M::T;
    using L = typename M::L;
    int sz, height{};
    vector<T> seg; vector<L> lazy;
    explicit LazySegmentTree(int n) {
        sz = 1;
        while(sz < n) sz <<= 1, height++;
        seg.assign(2*sz, M::e());
        lazy.assign(2*sz, M::l());
    }

    void set(int k, const T &x){
        seg[k + sz] = x;
    }

    void build(){
        for (int i = sz-1; i > 0; --i) seg[i] = M::f(seg[2*i], seg[2*i+1]);
    }

    T reflect(int k){ return lazy[k] == M::l() ? seg[k] : M::g(seg[k], lazy[k]); }

    void eval(int k){
        if(lazy[k] == M::l()) return;
        lazy[(k<<1)|0] = M::h(lazy[(k<<1)|0], lazy[k]);
        lazy[(k<<1)|1] = M::h(lazy[(k<<1)|1], lazy[k]);
        seg[k] = reflect(k);
        lazy[k] = M::l();
    }
    void thrust(int k){ for (int i = height; i; --i) eval(k>>i); }
    void recalc(int k) { while(k >>= 1) seg[k] = M::f(reflect((k<<1)|0), reflect((k<<1)|1));}
    void update(int a, int b, const L &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] = M::h(lazy[l], x), l++;
            if(r&1) --r, lazy[r] = M::h(lazy[r], x);
        }
        recalc(a);
        recalc(b);
    }

    T query(int a, int b){ // [l, r)
        thrust(a += sz);
        thrust(b += sz-1);
        T ll = M::e(), rr = M::e();
        for(int l = a, r = b+1; l < r; l >>=1, r>>=1) {
            if (l & 1) ll = M::f(ll, reflect(l++));
            if (r & 1) rr = M::f(reflect(--r), rr);
        }
        return M::f(ll, rr);
    }

    T operator[](const int &k) const { // 0-indexed
        return seg[k + sz];
    }
};

struct Monoid{
    using T = ll;
    using L = ll;
    static T f(T a, T b) { return min(a, b); }
    static T g(T a, L b) { return a+b; }
    static L h(L a, L b) { return a+b; }
    static T e() { return INF<int>; }
    static L l() { return 0; }
};

int main() {
    int n, q;
    cin >> n >> q;
    LazySegmentTree<Monoid> seg(n);
    for (int i = 0; i < n; ++i) {
        seg.set(i, 0);
    }
    seg.build();
    for (int i = 0; i < q; ++i) {
        int v;
        scanf("%d", &v);
        if(v == 0){
            int s, t; ll x;
            scanf("%d%d%lld", &s, &t, &x);
            seg.update(s, t+1, x);
        }else {
            int a, b;
            scanf("%d%d", &a, &b);
            printf("%lld\n", seg.query(a, b+1));
        }
    }
    return 0;
}