Problem: There is a sequence $A = a_0, a_1, ..., a_{n-1}$. You are given the following information and questions.

* relate$(x, y, z)$: $a_y$ is greater than $a_x$ by $z$
* diff$(x, y)$: report the difference between $a_x$ and $a_y$ $(a_y - a_x)$

Constraints

* $2 \leq n \leq 100,000$
* $1 \leq q \leq 200,000$
* $0 \leq x, y < n$
* $x \ne y$
* $0 \leq z \leq 10000$
* There are no inconsistency in the given information

Input


$n \; q$
$query_1$
$query_2$
:
$query_q$


In the first line, $n$ and $q$ are given. Then, $q$ information/questions are given in the following format.


0 $x \; y\; z$


or


1 $x \; y$


where '0' of the first digit denotes the relate information and '1' denotes the diff question.

Output

For each diff question, print the difference between $a_x$ and $a_y$ $(a_y - a_x)$.

Example

Input

5 6
0 0 2 5
0 1 2 3
1 0 1
1 1 3
0 1 4 8
1 0 4


Output

2
?
10

Solution (in PYTHON3):

Solution:
# Disjoint Set: Union Find Trees
[p, rank] = [[], []]
[n, q] = list(map(int, input().split()))
w = [0 for i in range(n)]

def makeSet(x):
    global p, rank
    p.append(x)
    rank.append(0)

def findSet(x):
    global p
    if x != p[x]:
        pre_parent = p[x]
        p[x] = findSet(p[x])
        w[x] += w[pre_parent]
    return p[x]

def link(x, y, z):
    global p, rank, w
    if rank[x] > rank[y]:
        p[y] = x
        w[y] = z
    else:
        p[x] = y
        w[x] = -z
        if rank[x] == rank[y]:
            rank[y] += 1

def same(x, y):
    if findSet(x) == findSet(y):
        return 1
    else:
        return 0   

def relate(x, y, z):
    global w
    root_x = findSet(x)
    root_y = findSet(y)
    z += w[x]
    z -= w[y]
    link(root_x, root_y, z)
   
def diff(x, y):
    if same(x, y) == 1:
        global w
        return w[y] - w[x]
    else:
        return "?"     

for i in range(n):
    makeSet(i)

for i in range(q):
    data = list(map(int, input().split()))
    if data[0] == 0:
        relate(data[1], data[2], data[3])
    else:
        print(diff(data[1], data[2]))