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:
// C++ 14
#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define loop(__x, __start, __end) for(ll __x = __start; __x < __end; __x++)

/* SegTreeLazy<X,M>(n,fx,fa,fm,ex,em): モノイド(集合X, 二項演算fx,fa,fm, 単位元ex,em)についてサイズnで構築
    
  using X = int;
  using M = int;
  auto fx = [](X x1, X x2) { return min(x1, x2); };
  auto fa = [](X x, M m) { return m; };
  auto fm = [](M m1, M m2) { return m2; };
  int ex = numeric_limits<int>::max();
  int em = numeric_limits<int>::max();
  SegTreeLazy<X, M> seg(n, fx, fa, fm, ex, em);
  set(int i, X x), build(): 初期化
  update(int a, int b, X x) 更新
*/
template <typename X, typename M>
struct SegTreeLazy {
    using FX = function<X(X, X)>;
    using FA = function<X(X, M)>;
    using FM = function<M(M, M)>;
    int n;
    FX fx;
    FA fa;
    FM fm;
    const X ex;
    const M em;
    vector<X> dat;
    vector<M> lazy;
    SegTreeLazy(int n_, FX fx_, FA fa_, FM fm_, X ex_, M em_)
        : n(), fx(fx_), fa(fa_), fm(fm_), ex(ex_), em(em_), dat(n_ * 4, ex), lazy(n_ * 4, em) {
        int x = 1;
        while (n_ > x) x *= 2;
        n = x;
    }
    void set(int i, X x) { dat[i + n - 1] = x; }
    void build() {
        for (int k = n - 2; k >= 0; k--) dat[k] = fx(dat[2 * k + 1], dat[2 * k + 2]);
    }
    /* lazy eval */
    void eval(int k) {
        if (lazy[k] == em) return;  // 更新するものが無ければ終了
        if (k < n - 1) {            // 葉でなければ子に伝搬
            lazy[k * 2 + 1] = fm(lazy[k * 2 + 1], lazy[k]);
            lazy[k * 2 + 2] = fm(lazy[k * 2 + 2], lazy[k]);
        }
        // 自身を更新
        dat[k] = fa(dat[k], lazy[k]);
        lazy[k] = em;
    }
    void update(int a, int b, M x, int k, int l, int r) {
        eval(k);
        if (a <= l && r <= b) {  // 完全に内側の時
            lazy[k] = fm(lazy[k], x);
            eval(k);
        } else if (a < r && l < b) {                     // 一部区間が被る時
            update(a, b, x, k * 2 + 1, l, (l + r) / 2);  // 左の子
            update(a, b, x, k * 2 + 2, (l + r) / 2, r);  // 右の子
            dat[k] = fx(dat[k * 2 + 1], dat[k * 2 + 2]);
        }
    }
    void update(int a, int b, M x) { update(a, b, x, 0, 0, n); }
    X query_sub(int a, int b, int k, int l, int r) {
        eval(k);
        if (r <= a || b <= l) {  // 完全に外側の時
            return ex;
        } else if (a <= l && r <= b) {  // 完全に内側の時
            return dat[k];
        } else {  // 一部区間が被る時
            X vl = query_sub(a, b, k * 2 + 1, l, (l + r) / 2);
            X vr = query_sub(a, b, k * 2 + 2, (l + r) / 2, r);
            return fx(vl, vr);
        }
    }
    X query(int a, int b) { return query_sub(a, b, 0, 0, n); }
};

/*
0 1 2 3 4 5 6
0 0 0 0 0 0 0
0 1 1 1 0 0 0
0 1-1-1-2 0 0 -> -2, 0
0 1-1 2 1 3 0 -> 1, -1
*/
int main() {
  int n, q; cin >> n >> q;
  using X = ll;
  using M = ll;
  const ll INF = (1LL<<31)-1;
  auto fx = [](X x1, X x2) { return min(x1, x2); };
  auto fa = [](X x, M m) { return x + m; };
  auto fm = [](M m1, M m2) { return m1 + m2; };
  X ex = INF;
  M em = 0;
  SegTreeLazy<X, M> seg(n+1, fx, fa, fm, ex, em);
  loop(i,0,n+1) seg.set(i, 0);
  seg.build();
  
  loop(i,0,q) {
    int com; cin >> com;
    if (com == 0)  {
      ll x, y, v; cin >> x >> y >> v;
      seg.update(x, y+1, v);
    }
    else {
      ll x, y; cin >> x >> y;
      cout << seg.query(x, y+1) << endl;
    }
  }
  return 0;
}