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
input = sys.stdin.readline

N,Q=map(int,input().split())

seg_el=1<<(N.bit_length()) # Segment treeの台の要素数
SEG=[0]*(2*seg_el) # 1-indexedなので、要素数2*seg_el.Segment treeの初期値で初期化
LAZY=[0]*(2*seg_el) # 1-indexedなので、要素数2*seg_el.Segment treeの初期値で初期化

def indexes(L,R): # 遅延伝搬すべきノードのリストを返す. （つまり, updateやgetvaluesで見るノードより上にあるノードたち）
    INDLIST=[]

    R-=1
    
    L>>=1
    R>>=1

    while L!=R:
        if L>R:
            INDLIST.append(L)
            L>>=1
        else:
            INDLIST.append(R)
            R>>=1

    while L!=0:
        INDLIST.append(L)
        L>>=1

    return INDLIST
        

def adds(l,r,x): # 区間[l,r)を +x 更新
        
    L=l+seg_el
    R=r+seg_el

    L//=(L & (-L))
    R//=(R & (-R))

    UPIND=indexes(L,R)
    
    while L!=R:
        if L > R:
            SEG[L]+=x
            LAZY[L]+=x
            L+=1
            L//=(L & (-L))

        else:
            R-=1
            SEG[R]+=x
            LAZY[R]+=x
            R//=(R & (-R))

    for ind in UPIND:
        SEG[ind]=min(SEG[ind<<1],SEG[1+(ind<<1)])+LAZY[ind]
        
def getvalues(l,r): # 区間[l,r)に関するminを調べる

    L=l+seg_el
    R=r+seg_el

    L//=(L & (-L))
    R//=(R & (-R))

    UPIND=indexes(L,R)
    
    for ind in UPIND[::-1]: # 遅延伝搬
        if LAZY[ind]!=0:
            plus_lazy=LAZY[ind]
            
            SEG[ind<<1]+=plus_lazy
            SEG[1+(ind<<1)]+=plus_lazy
            
            LAZY[ind<<1]+=plus_lazy
            LAZY[1+(ind<<1)]+=plus_lazy
            
            LAZY[ind]=0
            
    ANS=1<<31

    while L!=R:
        if L > R:
            ANS=min(ANS , SEG[L])
            L+=1
            L//=(L & (-L))

        else:
            R-=1
            ANS=min(ANS , SEG[R])
            R//=(R & (-R))

    return ANS

ANS=[]

for _ in range(Q):
    query=list(map(int,input().split()))
    if query[0]==0:
        adds(query[1],query[2]+1,query[3])

    else:
        ANS.append(getvalues(query[1],query[2]+1))

print("\n".join([str(ans) for ans in ANS]))