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<bits/stdc++.h>
using namespace std;

typedef long long ll;

#define p_ary(ary,a,b,i) do { cout << "["; for (int (i) = (a);(i) < (b);++(i)) cout << ary[(i)] << ((b)-1 == (i) ? "" : ", "); cout << "]\n"; } while(0)
#define p_map(map,it) do {cout << "{";for (auto (it) = map.begin();;++(it)) {if ((it) == map.end()) {cout << "}\n";break;}else cout << "" << (it)->first << "=>" << (it)->second << ", ";}}while(0)

struct LazySegmentTree {
private:
    int n;
    vector<ll> node,lazy;
public:
    LazySegmentTree(vector<ll> v) {
        int sz = v.size();
        n = 1;
        while (n < sz) n *= 2;
        node.resize(2*n-1);
        lazy.resize(2*n-1,0);
        for (int i = 0;i < sz;++i) node[i+n-1] = v[i];
        for (int i = n-2;i >= 0;--i) node[i] = min(node[i*2+1],node[i*2+2]);
    }

    void eval(int k,int l,int r) {
        if (lazy[k] != 0) {
            node[k] += lazy[k]/(r-l);
            if (r-l > 1) {
                lazy[2*k+1] += lazy[k]/2;
                lazy[2*k+2] += lazy[k]/2;
            }
            lazy[k] = 0;
        }
    }

    void add(int a,int b,ll x,int k = 0,int l = 0,int r = -1) {
        if (r < 0) r = n;
        eval(k,l,r);
        if (b <= l || r <= a) return;
        if (a <= l && r <= b) {
            lazy[k] += (r-l)*x;
            eval(k,l,r);
        } else {
            add(a,b,x,2*k+1,l,(l+r)/2);
            add(a,b,x,2*k+2,(l+r)/2,r);
            node[k] = min(node[2*k+1],node[2*k+2]);
        }
    }

    ll getmin(int a,int b,int k = 0,int l = 0,int r = -1) {
        if (r < 0) r = n;
        if (b <= l || r <= a) return INT64_MAX;
        eval(k,l,r);
        if (a <= l && r <= b) return node[k];
        ll vl = getmin(a,b,k*2+1,l,(l+r)/2);
        ll vr = getmin(a,b,2*k+2,(l+r)/2,r);
        return min(vl,vr);
    }
};

int main() {
    int n,q;
    cin >> n >> q;
    LazySegmentTree seg(vector<ll>(n,0));
    for (int i = 0;i < q;++i) {
        int c,s,t;
        cin >> c >> s >> t;
        if (c) cout << seg.getmin(s,t+1) << endl;
        else {
            int x;
            cin >> x;
            seg.add(s,t+1,x);
        }
    }
    return 0;
}