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;
using ll = long long;
const int segsize = 19;

ll SegTree[1<<segsize],Lazy[1<<segsize];
bool Flag[1<<segsize];
void denpa(int k,int l,int r)
{
	if(Flag[k])
	{
		SegTree[k]+=Lazy[k];
		//if(Lazy[k]!=INT_MAX)
		if(r-l>1)
		{
			Lazy[2*k] += Lazy[k];
			Lazy[2*k+1] += Lazy[k];
			Flag[k*2] = Flag[k*2+1]=true;
		}
		Lazy[k]=0;
		Flag[k] = false;

	}
}

void update(int a,int b,ll x,int k=1,int l=0,int r =-1)
{
	if(r<0)r=(1<<(segsize-1));
	//cout<<a<<' '<<b<<' '<<x<<' '<<k<<' '<<l<<' '<<r<<endl;
	denpa(k,l,r);
	if(b<=l||r<=a)return;
	if(a<=l&&r<=b)
	{
		Lazy[k] = (1LL)*x;
		Flag[k] = true;
		denpa(k,l,r);
	}
	else
	{
		update(a,b,x,k*2,l,(l+r)/2);
		update(a,b,x,k*2+1,(l+r)/2,r);
		SegTree[k] = min(SegTree[k*2],SegTree[k*2+1]);
	}
}

ll getsum(int a,int b,int k=1,int l=0,int r=-1)
{
	if(r<0)r = 1<<(segsize-1);
	denpa(k,l,r);
	if(b<=l||r<=a)return LLONG_MAX;
	if(a<=l&&r<=b)return SegTree[k];
	ll vl = getsum(a,b,k*2,l,(l+r)/2);
	ll vr = getsum(a,b,2*k+1,(l+r)/2,r);
	return min(vl,vr);
}

int main()
{
	for(int i = 0;i<(1<<segsize);i++)
	{
		SegTree[i]=0;
		Lazy[i] = 0;
	}
	int n,q;
	cin >> n >> q;
	for(int i = 0;i<q;i++)
	{
		int op;
		cin >> op;
		if(op)
		{
			int a,b;
			cin >> a >> b;
			
			cout<<getsum(a,b+1)<<endl;
		}
		else
		{
			int a,b,x;
			cin >> a >> b >> x;
			
			update(a,b+1,x);
		}
		//for (int i = 0; i < (1<<segsize); i++){cout<<SegTree[i]<<' '<<Lazy[i]<<endl;}cout<<endl;
		
		
	}
}