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;
#ifdef _DEBUG
#define _GLIBCXX_DEBUG
#include "dump.hpp"
#else
#define dump(...)
#endif

#define int long long
#define ll long long
#define DBG 1
#define rep(i, a, b) for (int i = (a); i < (b); i++)
#define rrep(i, a, b) for (int i = (b)-1; i >= (a); i--)
#define loop(n) rep(loop, (0), (n))
#define all(c) begin(c), end(c)
const int INF = sizeof(int) == sizeof(long long) ? 0x3f3f3f3f3f3f3f3fLL : 0x3f3f3f3f;
const int MOD = (int)(1e9) + 7;
#define fi first
#define se second
#define pb push_back
#define eb emplace_back
using pii = pair<int, int>;
// template<class T> ostream &operator<<(ostream &os,T &t){dump(t);return os;}
template <typename T, typename S>istream &operator>>(istream &is, pair<T, S> &p) { is >> p.first >> p.second; return is; }
//template <typename T, typename S>ostream &operator<<(ostream &os, pair<T, S> &p) {os << p.first << " " << p.second;return os;}

template <typename T> void printvv(const vector<vector<T>> &v) {
	cerr << endl;
	rep(i, 0, v.size()) rep(j, 0, v[i].size()) {
		if (typeid(v[i][j]).name() == typeid(INF).name() and v[i][j] == INF) {
			cerr << "INF";
		}
		else
			cerr << v[i][j];
		cerr << (j == v[i].size() - 1 ? '\n' : ' ');
	}
	cerr << endl;
}

#ifndef _DEBUG
#define printvv(...)
#endif
void YES(bool f) { cout << (f ? "YES" : "NO") << endl; }
void Yes(bool f) { cout << (f ? "Yes" : "No") << endl; }
template <class T, class U>bool chmin(T& a, U b) { if (a > b) { a = b; return true; }return false; }
template <class T, class U>bool chmax(T& a, U b) { if (a < b) { a = b; return true; }return false; }
struct RMQandRAQ {
	int n;
	vector<int>d, lazy, d2;
	RMQandRAQ(int m) {
		for (n = 1; n < m; n <<= 1);
		d.assign(2 * n, 0);
		d2.assign(2 * n, 0);
		lazy.assign(2 * n, 0);
	}
	void eval(int k, int l, int r) {
		if (lazy[k] != 0) {
			d[k] += lazy[k];
			d2[k] += lazy[k];
			if (r - l > 1) {
				lazy[2 * k] += lazy[k];
				lazy[2 * k + 1] += lazy[k];
			}
			lazy[k] = 0;
		}
	}
	void add(int a, int b, int x, int k = 1, int l = 0, int r = -1) {
		if (r == -1)r = n;
		eval(k, l, r);
		if (r <= a || b <= l)return;
		if (a <= l && r <= b) {
			lazy[k] += x;
			eval(k, l, r);
		}
		else {
			add(a, b, x, 2 * k, l, (l + r) / 2);
			add(a, b, x, 2 * k + 1, (l + r) / 2, r);
			d[k] = min(d[2 * k], d[2 * k + 1]);
			d2[k] = max(d2[2 * k], d2[2 * k + 1]);
		}
	}
	int getMin(int a, int b, int k = 1, int l = 0, int r = -1) {
		if (r == -1)r = n;
		eval(k, l, r);
		if (r <= a || b <= l)return INF;
		if (a <= l && r <= b)return d[k];
		else {
			int vl, vr;
			vl = getMin(a, b, 2 * k, l, (l + r) / 2);
			vr = getMin(a, b, 2 * k + 1, (l + r) / 2, r);
			return min(vl, vr);
		}
	}
	int getMax(int a, int b, int k = 1, int l = 0, int r = -1) {
		if (r == -1)r = n;
		eval(k, l, r);
		if (r <= a || b <= l)return -INF;
		if (a <= l && r <= b)return d2[k];
		else {
			int vl, vr;
			vl = getMax(a, b, 2 * k, l, (l + r) / 2);
			vr = getMax(a, b, 2 * k + 1, (l + r) / 2, r);
			return max(vl, vr);
		}
	}
};
signed main(signed argc, char *argv[]) {
	cin.tie(0);
	ios::sync_with_stdio(false);
	cout << fixed << setprecision(12);

	int N; cin >> N;
	int Q; cin >> Q;
	RMQandRAQ seg(N);
	loop(Q) {
		int com; cin >> com;
		if (com) {
			int s, t; cin >> s >> t;
			cout << seg.getMin(s, t + 1) << endl;
		}
		else {
			int s, t, x; cin >> s >> t >> x;
			seg.add(s, t + 1, x);
		}
	}

	return 0;
}