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 <string>
#include <utility>
#include <algorithm>
#include <map>
#include <set>
#include <vector>
#include <cmath>
#include <cstdlib>
#include <queue>
#include <stack>
#include <iomanip>
#include <fstream>

using namespace std;

#define REP(i, n) for(ll i = 0;i < n;i++)
#define REPR(i, n) for(ll i = n;i >= 0;i--)
#define FOR(i, m, n) for(ll i = m;i < n;i++)
#define FORR(i, m, n) for(ll i = m;i >= n;i--)
#define REPO(i, n) for(ll i = 1;i <= n;i++)
#define ll long long
#define INF (ll)1 << 60
#define MINF (-1 * INF)
#define ALL(n) n.begin(),n.end()
#define MOD 1000000007
#define P pair<ll, ll>

struct LazySegTree {
	ll sz;
	vector<ll> dat, lazy;
	LazySegTree(ll n) {
		sz = 1;
		while (sz < n)sz *= 2;
		dat.resize(2 * sz - 1);
		lazy.resize(2 * sz - 1);
	}
	void eval(ll k, ll l, ll r) {
		if (lazy[k] != 0) {
			dat[k] += lazy[k];
			if (r - l > 1) {
				lazy[k * 2 + 1] += lazy[k];
				lazy[k * 2 + 2] += lazy[k];
			}
			lazy[k] = 0;
		}
	}
	void update(ll a, ll b, ll x, ll k = 0, ll l = 0, ll r = -1) {
		if (r < 0)r = sz;
		eval(k, l, r);
		if (r <= a or b <= l) return;
		if (a <= l and r <= b) {
			lazy[k] += x;
			eval(k, l, r);
		}
		else {
			update(a, b, x, k * 2 + 1, l, (l + r) / 2);
			update(a, b, x, k * 2 + 2, (l + r) / 2, r);
			dat[k] = min(dat[k * 2 + 1], dat[k * 2 + 2]);
		}
	}
	ll query(ll a, ll b, ll k = 0, ll l = 0, ll r = -1) {
		if (r < 0)r = sz;
		if (r <= a or b <= l)return INF;
		eval(k, l, r);
		if (a <= l and r <= b) return dat[k];
		ll q1, q2;
		q1 = query(a, b, k * 2 + 1, l, (l + r) / 2);
		q2 = query(a, b, k * 2 + 2, (l + r) / 2, r);
		return min(q1, q2);
	}
};
int main() {
	ll n, q;
	cin >> n >> q;
	LazySegTree s(n * 2);
	REP(i, q) {
		ll t;
		cin >> t;
		if (t == 0) {
			ll a, b, c;
			cin >> a >> b >> c;
			b++;
			s.update(a, b, c);
		}
		else {
			ll a, b;
			cin >> a >> b;
			b++;
			cout << s.query(a, b) << endl;
		}
	}
}