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 <vector>
#include <string>
#include <cmath>
#include <cstring>
#include <utility>
#include <numeric>

using namespace std;

// LazyAddSegmentTree
template<typename T>
class LazyAddSegTree{
public:
    int n;
    T defaultValue;
    vector<T> dat;
    vector<T> lazy;

    LazyAddSegTree(vector<T>& v, T defaultValue){
        n = 1;
        int vSize = (int)v.size();
        while(n < vSize){
            n *= 2;
        }
        dat.assign(2 * n - 1, defaultValue);
        lazy.assign(2 * n - 1, 0);
        this->defaultValue = defaultValue;

        for(int i = 0; i < vSize; i++){
            dat[i + n - 1] = v[i];
        }
        for(int i = n - 2; i >= 0; i--){
            dat[i] = ope(dat[2 * i + 1], dat[2 * i + 2]);
        }
    }

    T add(int a, int b, T value, int k = 0, int l = 0, int r = -1){
        if(r < 0){
            r = n;
        }
        propagate(k);

        if(r <= a || b <= l){
            return dat[k];
        }

        if(a <= l && r <= b){
            lazy[k] += lazyPlus(value, l, r);
            propagate(k);
            return dat[k];
        }
        else{
            T vl = add(a, b, value, 2 * k + 1, l, (l + r) / 2);
            T vr = add(a, b, value, 2 * k + 2, (l + r) / 2, r);
            dat[k] = ope(vl, vr);
            return dat[k];
        }
    }

    T query(int a, int b, int k = 0, int l = 0, int r = -1){
        if(r < 0){
            r = n;
        }

        if(r <= a || b <= l){
            return defaultValue;
        }
        propagate(k);

        if(a <= l && r <= b){
            return dat[k];
        }
        else{
            T vl = query(a, b, 2 * k + 1, l, (l + r) / 2);
            T vr = query(a, b, 2 * k + 2, (l + r) / 2, r);
            return ope(vl, vr);
        }
    }

private:

    void propagate(int k){
        if(lazy[k] != 0){
            dat[k] += lazy[k];
            if(k <= n - 2){
                T value = lazyPropPlus(lazy[k]);
                lazy[2 * k + 1] += value;
                lazy[2 * k + 2] += value;
            }

            lazy[k] = 0;
        }
    }

    T ope(T a, T b){
        return min(a, b);
    }

    T lazyPlus(T value, int l, int r){
        return value;
    }

    T lazyPropPlus(T value){
        return value;
    }
};

int main(){

    int n, q;
    cin >> n >> q;

    vector<long long> v(n, 0);
    const long long INF = (1LL << 60);
    LazyAddSegTree<long long> lazySegTree(v, INF);

    for(int loop = 0; loop < q; loop++){
        int com;
        cin >> com;
        if(com == 0){
            int s, t, x;
            cin >> s >> t >> x;
            lazySegTree.add(s, t + 1, x);
        }
        else{
            int s, t;
            cin >> s >> t;
            cout << lazySegTree.query(s, t + 1) << endl;
        }
    }

    return 0;
}