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;

struct RMQ {
	using type = int;
	static type id() { return INT_MAX; }
	static type op(const type& l, const type & r) { return min(l, r); }
};

template <typename M>
class StarrySkyTree {
	using T = typename M::type;
	const int n;
	vector<T> data, lazy;
	int size(int n) {
		int res = 1;
		while (res < n) res <<= 1;
		return res;
	}
	T sub(int l, int r, int node, int lb, int ub) {
		if (r <= lb || ub <= l) return M::id();
		if (l <= lb && ub <= r) return data[node];
		return M::op(sub(l, r, node << 1, lb, (lb + ub) >> 1)
			, sub(l, r, (node << 1) | 1, (lb + ub) >> 1, ub)) + lazy[node];
	}
	void suc(int l, int r, int node, int lb, int ub, T val) {
		if (ub <= l || r <= lb) return;
		if (l <= lb && ub <= r) {
			data[node] += val;
			lazy[node] += val;
			return;
		}
		suc(l, r, node << 1, lb, (lb + ub) >> 1, val);
		suc(l, r, (node << 1) | 1, (lb + ub) >> 1, ub, val);
		data[node] = M::op(data[node << 1], data[(node << 1) | 1]) + lazy[node];
	}
public:
	StarrySkyTree(int n_) : n(size(n_)), data(n << 1), lazy(n << 1) {}
	void add(int l, int r, T val) {
		suc(l, r + 1, 1, 0, n, val);
	}
	T find(int l, int r) {
		return sub(l, r + 1, 1, 0, n);
	}
};

int main()
{
	ios::sync_with_stdio(false), cin.tie(0);
	int n, q;
	cin >> n >> q;
	StarrySkyTree<RMQ> sst(n);
	while (q--) {
		int com;
		cin >> com;
		if (com == 0) {
			int s, t, x;
			cin >> s >> t >> x;
			sst.add(s, t, x);
		}
		else {
			int s, t;
			cin >> s >> t;
			printf("%d\n", sst.find(s, t));
		}
	}
	return 0;
}