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 <vector>
#include <map>
#include <unordered_map>
#include <queue>
#include <set>
#include <algorithm>
#include <string>
#include <math.h>
#include <limits.h>
#include <stack>
#include <complex>
#include <stdlib.h>
#include <stdio.h>
#include <functional>
#include <cfloat>


#define fs first
#define sc second

using namespace std;

typedef long long ll;
typedef pair<ll, ll> P;


const ll MAX_N = 151000;

template<typename T>
class LazySegmentTree{
public:
    //セグメント木を持つグローバル変数
    int n;
    T node[2 * MAX_N - 1];
    T lazy[2 * MAX_N - 1];

    void init(int n_, T init_num){
        n = 1;
        while(n < n_) n *= 2;
        for(int i = 0; i < 2*n-1; i++){
            node[i] = init_num;
            lazy[i] = 0;
        }
    }

    void eval(int k, int l, int r){
        if(lazy[k] != 0){
            node[k] += lazy[k];

            if(r - l > 1){
                lazy[2*k+1] += lazy[k];
                lazy[2*k+2] += lazy[k];
            }
            lazy[k] = 0;
        }
    }

    void add(int a, int b, int k, int l, int r, T x){
        eval(k, l, r);
        if(r <= a || b <= l){
            return;
        }

        if (a <= l && r <= b) {
            lazy[k] = x;
            eval(k, l, r);
        }
        else{
            add(a, b, 2*k+1, l, (l+r)/2, x);
            add(a, b, 2*k+2, (l+r)/2, r, x);
            node[k] = min(node[2*k+1], node[2*k+2]);
        }
    }


    // [a, b)の最小値を求める。
    // kは節点の番号、l, rはその節点が[l, r)に対応づいていることを表す。
    // query(a, b, 0, 0, n)で外からは呼び出す。
    ll query(int a, int b, int k, int l, int r) {
        if (r <= a || b <= l) {
            return LONG_LONG_MAX;
        }

        eval(k, l, r);
        if (a <= l && r <= b) {
            return node[k];
        } else {
            ll vl = query(a, b, k * 2 + 1, l, (l + r) / 2);
            ll vr = query(a, b, k * 2 + 2, (l + r) / 2, r);
            return min(vl, vr);
        }
    }
};


int main(){
    ll N, M;
    cin >> N >> M;

    LazySegmentTree<ll> st;
    st.init(N, 0);
    for(int i = 0; i < M; i++){
        int q, s, t, x;
        cin >> q;
        if(q == 0) {
            cin >> s >> t >> x;
            st.add(s, t+1, 0, 0, st.n, x);
        }
        else{
            cin >> s >> t;
            cout << st.query(s, t+1, 0, 0, st.n) << endl;

        }
    }


    return 0;

}