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<iomanip>
#include <cmath>
#include <climits>
#include <algorithm>
#include <stdio.h>
#include <vector>
#include <queue>
#include <tuple>
#include <map>
#include <list>
#include <string>
#include <numeric>
#include <utility>
#include <cfloat>
#include <set>
 
using namespace std;
 
int sqrtN = 320;
struct SqrtDecomposition{
    int N, K;
    vector <long long> data;
    //vector <long long> bucketUpdatedLazy;
    vector <long long> bucketAdded;
    vector <long long> bucketMin;
    
    SqrtDecomposition(int n){
        N = n;
        K = (N + sqrtN - 1) / sqrtN;
        data.assign(N + sqrtN, 0);
        //bucketUpdatedLazy.assign(K, -1);
        bucketMin.assign(K, 0);
        bucketAdded.assign(K, 0);
    }
 
    /*
    void propagateLazy(int k){
        if(bucketUpdatedLazy[k] < 0){
            return;
        }
        for(int i = 0; i < sqrtN; i++){
            data[k * sqrtN + i] = bucketUpdatedLazy[k];
        }
        bucketMin[k] = bucketUpdatedLazy[k];
        bucketUpdatedLazy[k] = -1;
    }
    */

    void updateMin(int k){
        bucketMin[k] = data[k * sqrtN];
        for(int i = 0; i < sqrtN; i++){
            bucketMin[k] = min(data[k * sqrtN + i], bucketMin[k]);
        }
    }

    long long get(int x){
        return data[x] + bucketAdded[x / sqrtN];
    }
    
    long long find(int x, int y){
        //propagateLazy(x / sqrtN);
        //propagateLazy((y - 1) / sqrtN);
        long long ans = data[x] + bucketAdded[x / sqrtN];
        if(y - x < sqrtN){
            for(int i = x; i < y; i++){
                ans = min(ans, data[i] + bucketAdded[i / sqrtN]);
            }
            return ans;
        }
        for(int i = x / sqrtN + 1; i < y / sqrtN; i++){
            ans = min(ans, bucketMin[i] + bucketAdded[i]);
        }

        for(int i = x; i < (x / sqrtN + 1) * sqrtN; i++){
            ans = min(ans, data[i] + bucketAdded[i / sqrtN]);
        }
        for(int i = y / sqrtN * sqrtN; i < y; i++){
            ans = min(ans, data[i] + bucketAdded[i / sqrtN]);
        }
        return ans;
    }
 

    void add(int x, int y, long long a){
        if(y - x < sqrtN){
            for(int i = x; i < y; i++){
                data[i] += a;
            }
            updateMin(x / sqrtN);
            updateMin((y - 1) / sqrtN);
            return;
        }
        for(int i = x / sqrtN + 1; i < y / sqrtN; i++){
            bucketAdded[i] += a;
        }

        //propagateLazy(x / sqrtN);
        for(int i = x; i < (x / sqrtN + 1) * sqrtN; i++){
            data[i] += a;
        }
        updateMin(x / sqrtN);
        //propagateLazy((y - 1)/ sqrtN);
        for(int i = y / sqrtN * sqrtN; i < y; i++){
            data[i] += a;
        }
        updateMin((y - 1) / sqrtN);
    }
     
};

int main(){
    int n;
    int q;
    cin >> n >> q;
    SqrtDecomposition sq(n);
    for(int i = 0; i < q; i++){
        int com;
        int s;
        int t;
        int x;
        cin >> com;
        if(com == 0){
            cin >> s >> t >> x;
            sq.add(s, t + 1, x);
        } else {
            cin >> s >> t;
            cout << sq.find(s, t + 1) << endl;
        }
    }
    return 0;
}