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 <vector>
#include <functional>
#include <cassert>
#include <algorithm>
using namespace std;

template <class T> class RAQ_and_RmQ {
	int n;
	T init;
	vector<T> node, lazy;
	static int ceil2(int n) {
		int m = 1;
		while (m < n) m *= 2;
		return m;
	}
	void eval(int k, int l, int r) {
		if (lazy[k] != 0) {
			node[k] += lazy[k];
			if (r - l > 1) {
				lazy[2 * k + 0] += lazy[k];
				lazy[2 * k + 1] += lazy[k];
			}
			lazy[k] = 0;
		}
	}
	void add_impl(int a, int b, const T& x, int k, int l, int r) {
		eval(k, l, r);
		if (b <= l || r <= a) {
			return;
		} else if (a <= l && r <= b) {
			lazy[k] += x;
			eval(k, l, r);
		} else {
			add_impl(a, b, x, 2 * k + 0, l, (l + r) / 2);
			add_impl(a, b, x, 2 * k + 1, (l + r) / 2, r);
			node[k] = min(node[2 * k + 0], node[2 * k + 1]);
		}
	}
	T query_impl(int a, int b, int k, int l, int r) {
		if (b <= l || r <= a) {
			return init;
		}
		eval(k, l, r);
		if (a <= l && r <= b) {
			return node[k];
		} else {
			auto vl = query_impl(a, b, 2 * k + 0, l, (l + r) / 2);
			auto vr = query_impl(a, b, 2 * k + 1, (l + r) / 2, r);
			return min(vl, vr);
		}
	}

public:
	RAQ_and_RmQ(const vector<T>& vec, const T& _init) : init(_init) {
		build(vec);
	}
	void build(const vector<T>& v) {
		n = ceil2(v.size());
		node.assign(n * 2, init);
		lazy.assign(n * 2, 0);
		for (int i = 0; i < v.size(); ++i) {
			node[i + n] = v[i];
		}
		for (int i = n - 1; i > 0; --i) {
			node[i] = min(node[i * 2 + 0], node[i * 2 + 1]);
		}
	}
	void add(int l, int r, const T& x) {
		add_impl(l, r, x, 1, 0, n);
	}
	T operator[](int i) {
		assert(0 <= i && i < n);
		return operator()(i, i + 1);
	}
	T operator()(int l, int r) {
		assert(0 <= l && l < r && r <= n);
		return query_impl(l, r, 1, 0, n);
	}
	vector<T> to_a() {
		vector<T> res(n);
		for (int i = 0; i < n; ++i) {
			res[i] = operator[](i);
		}
		return res;
	}
};

using ll = long long;

int main() {
	ios::sync_with_stdio(false);
	cin.tie(nullptr);
	int n, q;
	cin >> n >> q;
	RAQ_and_RmQ<ll> seg(vector<ll>(n, 0), 1e9);
	for (int i = 0; i < q; ++i) {
		int com;
		cin >> com;
		if (com == 0) {
			int s, t;
			ll x;
			cin >> s >> t >> x;
			seg.add(s, t + 1, x);
		} else if (com == 1) {
			int s, t;
			cin >> s >> t;
			cout << seg(s, t + 1) << '\n';
		}
	}
}