Problem:
Weighted Union Find Trees

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 $a_y$ $(a_y - a_x)$

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 $a_y$ $(a_y - a_x)$.

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

Sample Input

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

Sample Output

2
?
10

Solution in Ruby (judge verdict: Accepted)

def get_height x
    px, hx = x, 0
    while px != @parent[px][0]
        hx += @parent[px][1]
        px = @parent[px][0]
    end
    return [px, hx]
end

n, q = gets.chomp.split.map(&:to_i)

@parent = []
0.upto(n - 1){|i| @parent[i] = [i, 0]}

q.times{
    command, x, y, z = gets.chomp.split.map(&:to_i)
    px, hx = get_height(x)
    py, hy = get_height(y)

    case command
    when 0
        next if px == py
        if px < py
            @parent[py] = px, hx - hy + z
        else
            @parent[px] = py, hy - hx - z
        end
    when 1
        puts (px != py) ? "?" : hy - hx
    end
}