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 int ll;
typedef vector<ll> vl;
typedef pair<ll, ll> PP;
#define rep(i, n) for(ll i = 0; i < ll(n); i++)
#define all(v) v.begin(), v.end()
bool chmin(ll & a, ll  b) { if (b < a) { a = b; return 1; } return 0; }
bool chmax(ll & a, ll b) { if (b > a) { a = b; return 1; } return 0; }
const ll INF = (1LL<<31)-1;
const ll MOD = 1000000007;
const ll MAX_N=500010;
ll a, b, c, d, e, f, p, t, x, y, z, q, m, n, r, h, k, w, l, ans;
template <typename T,typename E>
struct SegmentTree{
  typedef function<T(T,T)> F;
  typedef function<T(T,E)> G;
  typedef function<E(E,E)> H;
  typedef function<E(E,ll)> P;
  ll n;
  F f;
  G g;
  H h;
  P p;
  T d1;
  E d0;
  vector<T> dat;
  vector<E> laz;
  SegmentTree(ll n_,F f,G g,H h,T d1,E d0,
	      vector<T> v=vector<T>(),P p=[](E a,ll b){return a;}):
    f(f),g(g),h(h),d1(d1),d0(d0),p(p){
    init(n_);
    if(n_==(ll)v.size()) build(n_,v);
  }
  void init(ll n_){
    n=1;
    while(n<n_) n*=2;
    dat.clear();
    dat.resize(2*n-1,d1);
    laz.clear();
    laz.resize(2*n-1,d0);
  }
  void build(ll n_, vector<T> v){
    for(ll i=0;i<n_;i++) dat[i+n-1]=v[i];
    for(ll i=n-2;i>=0;i--)
      dat[i]=f(dat[i*2+1],dat[i*2+2]);
  }
  inline void eval(ll len,ll k){
    if(laz[k]==d0) return;
    if(k*2+1<n*2-1){
      laz[k*2+1]=h(laz[k*2+1],laz[k]);
      laz[k*2+2]=h(laz[k*2+2],laz[k]);
    }
    dat[k]=g(dat[k],p(laz[k],len));
    laz[k]=d0;
  }
  T update(ll a,ll b,E x,ll k,ll l,ll r){
    eval(r-l,k);
    if(r<=a||b<=l) return dat[k];
    if(a<=l&&r<=b){
      laz[k]=h(laz[k],x);
      return g(dat[k],p(laz[k],r-l));
    }
    return dat[k]=f(update(a,b,x,k*2+1,l,(l+r)/2),
		    update(a,b,x,k*2+2,(l+r)/2,r));
  }
  T update(ll a,ll b,E x){
    return update(a,b,x,0,0,n);
  }
  T query(ll a,ll b,ll k,ll l,ll r){
    eval(r-l,k);
    if(r<=a||b<=l) return d1;
    if(a<=l&&r<=b) return dat[k];
    T vl=query(a,b,k*2+1,l,(l+r)/2);
    T vr=query(a,b,k*2+2,(l+r)/2,r);
    return f(vl,vr);
  }
  T query(ll a,ll b){
    return query(a,b,0,0,n);
  }
};
    auto F = [](ll a, ll b){return min(a,b);};
    auto G = [](ll a, ll b){return a+b;};
    auto H = G;
    SegmentTree<ll,ll> seg(MAX_N, F, G, H, INF, 0,vl(MAX_N,0));
int main() { cin >> n >> q; 
while(q--){
    cin >> x;
    if(x==0){
        cin >> a >> b >> c;
        seg.update(a, b + 1, c);
    }
    else{
        cin >> a >> b;
        cout << seg.query(a, b + 1)<<endl;
    }
}}