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 ll;
#define rep(i, n) for(ll i = 0, i##_len = (n); i < i##_len; i++)
#define reps(i, s, n) for(ll i = (s), i##_len = (n); i < i##_len; i++)
#define rrep(i, n) for(ll i = (n) - 1; i >= 0; i--)
#define rreps(i, e, n) for(ll i = (n) - 1; i >= (e); i--)
#define all(x) (x).begin(), (x).end()
#define sz(x) ((ll)(x).size())
#define len(x) ((ll)(x).length())

template<class T>
struct LazySegmentTree {
private:
    int n;
    vector<T> node, lazy;
    vector<bool> updated;
    T def;
    function<T(T,T)> out;
    function<T(T,T,int)> app;
    
    void init(const vector<T> &v, T _def, function<T(T,T,int)> _app, function<T(T,T)> _out) {
        def = _def; out = _out; app = _app;
        int vl = (int)v.size();
        n = 1; while(n < vl) n *= 2;
        node.resize(2 * n - 1, def);
        lazy.resize(2 * n - 1, 0);
        updated.resize(2 * n - 1, false);
        for(int i = 0; i < vl; i++) node[i + n - 1] = v[i];
        for(int i = n - 2; i >= 0; i--) node[i] = out(node[i * 2 + 1], node[i * 2 + 2]);
    }
    
    void eval(int k, int l, int r) {
        if (updated[k]) {
            node[k] = app(node[k], lazy[k], r - l);
            if ((r - l) > 1) {
                lazy[k * 2 + 1] += lazy[k];
                lazy[k * 2 + 2] += lazy[k];
                updated[k * 2 + 1] = updated[k * 2 + 2] = true;
            }
            lazy[k] = 0;
            updated[k] = false;
        }
    }
    
public:
    LazySegmentTree() {}
    LazySegmentTree(int _n, T _def, function<T(T,T,int)> _app, function<T(T,T)> _out) {
        init(vector<T>(_n, _def), _def, _app, _out);
    }
    LazySegmentTree(const vector<T> &v, T _def, function<T(T,T,int)> _app, function<T(T,T)> _out) {
        init(v, _def, _app, _out);
    }
    
    void update(int a, int b, T x, int k = 0, int l = 0, int r = -1) {
        if (r < 0) r = n;
        eval(k, l, r);
        if((b <= l) || (r <= a)) return;
        if((a <= l) && (r <= b)) {
            lazy[k] += x;
            updated[k] = true;
            eval(k, l, r);
        }
        else {
            update(a, b, x, 2 * k + 1, l, (l + r) / 2);
            update(a, b, x, 2 * k + 2, (l + r) / 2, r);
            node[k] = out(node[2 * k + 1], node[2 * k + 2]);
        }
    }
    
    T query(int a, int b, int k = 0, int l = 0, int r = -1) {
        if (r < 0) r = n;
        eval(k, l, r);
        if ((b <= l) || (r <= a)) return def;
        if ((a <= l) && (r <= b)) return node[k];
        T vl = query(a, b, 2 * k + 1, l, (l + r) / 2);
        T vr = query(a, b, 2 * k + 2, (l + r) / 2, r);
        return out(vl, vr);
    }
};

int main() {
    cin.tie(0);
    ios::sync_with_stdio(false);
    // ifstream in("input.txt");
    // cin.rdbuf(in.rdbuf());
    const ll inf = LONG_LONG_MAX / 2 - 1;
    ll n, q;
    cin >> n >> q;
    LazySegmentTree<ll> lst(vector<ll>(n, 0), inf, [](ll a, ll b, ll c){ return a + b; }, [](ll a, ll b){ return min(a, b); });
    rep(i, q) {
        ll com;
        cin >> com;
        if (com == 0) {
            ll s, t, x;
            cin >> s >> t >> x;
            lst.update(s, t + 1, x);
        }
        else {
            ll s, t;
            cin >> s >> t;
            cout << lst.query(s, t + 1) << endl;
        }
    }
    return 0;
}