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 PYTHON3):

Solution:
import sys
class Lazysegtree:
    #RAQ
    def __init__(self, A, intv, initialize = True, segf = min):
        #区間は 1-indexed で管理
        self.N = len(A)
        self.N0 = 2**(self.N-1).bit_length()
        self.intv = intv
        self.segf = segf
        self.lazy = [0]*(2*self.N0)
        if initialize:
            self.data = [intv]*self.N0 + A + [intv]*(self.N0 - self.N)
            for i in range(self.N0-1, 0, -1):
                self.data[i] = self.segf(self.data[2*i], self.data[2*i+1]) 
        else:
            self.data = [intv]*(2*self.N0)

    def _ascend(self, k):
        k = k >> 1
        c = k.bit_length()
        for j in range(c):
            idx = k >> j
            self.data[idx] = self.segf(self.data[2*idx], self.data[2*idx+1]) \
            + self.lazy[idx]
            
    def _descend(self, k):
        k = k >> 1
        idx = 1
        c = k.bit_length()
        for j in range(1, c+1):
            idx = k >> (c - j)
            ax = self.lazy[idx]
            if not ax:
                continue
            self.lazy[idx] = 0
            self.data[2*idx] += ax
            self.data[2*idx+1] += ax
            self.lazy[2*idx] += ax
            self.lazy[2*idx+1] += ax
    
    def query(self, l, r):
        L = l+self.N0
        R = r+self.N0
        Li = L//(L & -L)
        Ri = R//(R & -R)
        self._descend(Li)
        self._descend(Ri - 1)
        
        s = self.intv                                                              
        while L < R:
            if R & 1:
                R -= 1
                s = self.segf(s, self.data[R])
            if L & 1:
                s = self.segf(s, self.data[L])
                L += 1
            L >>= 1
            R >>= 1
        return s
    
    def update(self, l, r, x):
        L = l+self.N0
        R = r+self.N0

        Li = L//(L & -L)
        Ri = R//(R & -R)
        
        while L < R :
            if R & 1:
                R -= 1
                self.data[R] += x
                self.lazy[R] += x
            if L & 1:
                self.data[L] += x
                self.lazy[L] += x
                L += 1
            L >>= 1
            R >>= 1
        
        self._ascend(Li)
        self._ascend(Ri-1)

N, Q = map(int, input().split())
T = Lazysegtree([0]*N, 2<<31) 
Ans = []
for jq in range(Q):
    t, *q = map(int, sys.stdin.readline().split())
    q[1] += 1
    if t:
        Ans.append(T.query(*q))
    else:
        T.update(*q)
print('\n'.join(map(str, Ans)))