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:

def union(x, y, t):
    x, t_x = findSet(x)
    y, t_y = findSet(y)
    link(x, t_x, y, t_y, t)


def link(x, d_x, y, d_y, t):
    #print('', 'x', 'y')
    #print('', x, y)
    #print('', d_x, d_y, t)
    if r[x] > r[y]:
        p[y] = x
        d[y] = d_x - d_y - t
        #print('', y, '->', p[y], '=', d[y], '\n')

    else:
        p[x] = y
        d[x] = d_y - d_x + t
        if r[x] == r[y]: r[y] = r[y] + 1
        #print('', x, '->', p[x], '=', d[x], '\n')


def findSet(x):
    if x != p[x]:
        p[x], t = findSet(p[x])
        d[x] += t
    return p[x], d[x]


def diff(x, y):
    x, d_x = findSet(x)
    y, d_y = findSet(y)
    if x == y:
        return d_x - d_y

    else:
        return '?'




if __name__ == '__main__':

    p, r, d = [], [], []

    n_set, n_quare = map(int, input().split())

    for i in range(n_set):
        p.append(i)
        r.append(0)
        d.append(0)


    for i in range(n_quare):
        l = input().split()

        if len(l) == 4:
            _, x, y, t = map(int, l)
            union(x, y, t)

        else:
            _, x, y = map(int, l)
            print(diff(x, y))