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 <stdio.h>
#include <string.h>
const int N=1e5+10;
const int INF=1e9+10;
int val[N*4],flag[N*4];
int min(int a,int b){return a>b?b:a;}
void add(int now,int l,int r,int L,int R,int n){
    if(L<=l&&r<=R){
        val[now]+=n;
        flag[now]+=n;
    }
    else if(!(L>r||l>R)){
        int mid=(l+r)>>1;
        if(flag[now]!=0){
            flag[now*2+1]+=flag[now];
            flag[now*2+2]+=flag[now];
            val[now*2+2]+=flag[now];
            val[now*2+1]+=flag[now];
            flag[now]=0;
        }
        add(now*2+1,l,mid,L,R,n);
        add(now*2+2,mid+1,r,L,R,n);
        val[now]=min(val[now*2+1],val[now*2+2]);
    }
    return ;
}
int query(int now,int l,int r,int L,int R){
    int ans=INF;
    if(L<=l&&r<=R)ans=val[now];
    else if(!(L>r||l>R)){
        int mid=(l+r)>>1;
        if(flag[now]!=0){
            flag[now*2+1]+=flag[now];
            flag[now*2+2]+=flag[now];
            val[now*2+2]+=flag[now];
            val[now*2+1]+=flag[now];
            flag[now]=0;
        }
        ans=min(query(now*2+1,l,mid,L,R),query(now*2+2,mid+1,r,L,R));
    }
    return ans;
}
int main(){
    int n,q,k,l,r;
    scanf("%d%d",&n,&q);
    memset(val,0,sizeof(val));
    memset(flag,0,sizeof(flag));
    while(q--){
        scanf("%d%d%d",&k,&l,&r);
        if(k==0){
            scanf("%d",&k);
            add(0,0,n,l,r,k);
        }
        else printf("%d\n",query(0,0,n,l,r));
    }
    
}