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;
#define rep(i,N) for(int i=0;i<(int)N;++i)
#define rep1(i,N) for(int i=1;i<=(int)N;++i)
#define all(x) x.begin(),x.end()
#define rall(x) x.rbegin(),x.rend()
#define SZ(x) (int)x.size()
#define e_b emplace_back
using ll = long long;
const ll LINF=1LL<<60;
const int INF=1<<30;

struct StarrySkyTree{
	int n;
	vector<int> node,lazy;
	
	StarrySkyTree(int sz){
		n=1;
		while(sz>n) n<<=1;
		node.assign(2*n,0);
		lazy.assign(2*n,0);
	}
	
	void eval(int k,int l,int r){
		if(lazy[k]){
			node[k]+=lazy[k];
			if(r-l>1){
				lazy[2*k]+=lazy[k];
				lazy[2*k+1]+=lazy[k];
			}
			lazy[k]=0;
		}
	}
	
	void add(int a,int b,int x,int k=1,int l=0,int r=-1){
		if(r<0) r=n;
		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,x,2*k,l,(l+r)/2);
			add(a,b,x,2*k+1,(l+r)/2,r);
			node[k]=min(node[2*k],node[2*k+1]);
		}
	}
	
	int getMin(int a,int b,int k=1,int l=0,int r=-1){
		if(r<0) r=n;
		eval(k,l,r);
		if(r<=a||b<=l) return INF;
		if(a<=l&&r<=b) return node[k];
		else{
			int vl=getMin(a,b,2*k,l,(l+r)/2);
			int vr=getMin(a,b,2*k+1,(l+r)/2,r);
			return min(vl,vr);
		}
	}
};

int main(){
	int n,q; cin>>n>>q;
	StarrySkyTree tree(n);
	rep(i,q){
		int m,s,t,x;
		cin>>m;
		if(m==0){
			cin>>s>>t>>x;
			tree.add(s,t+1,x);
		}else{
			cin>>s>>t;
			cout<<tree.getMin(s,t+1)<<endl;
		}
	}
}