You are given a connected undirected graph consisting of $$$n$$$ vertices and $$$m$$$ edges. The weight of the $$$i$$$-th edge is $$$i$$$.

Here is a wrong algorithm of finding a minimum spanning tree (MST) of a graph:


vis := an array of length n
s := a set of edges

function dfs(u):
    vis[u] := true
    iterate through each edge (u, v) in the order from smallest to largest edge weight
        if vis[v] = false
            add edge (u, v) into the set (s)
            dfs(v)

function findMST(u):
    reset all elements of (vis) to false
    reset the edge set (s) to empty
    dfs(u)
    return the edge set (s)

Each of the calls findMST(1), findMST(2), ..., findMST(n) gives you a spanning tree of the graph. Determine which of these trees are minimum spanning trees.

Input

The first line of the input contains two integers $$$n$$$, $$$m$$$ ($$$2\le n\le 10^5$$$, $$$n-1\le m\le 2\cdot 10^5$$$) — the number of vertices and the number of edges in the graph.

Each of the following $$$m$$$ lines contains two integers $$$u_i$$$ and $$$v_i$$$ ($$$1\le u_i, v_i\le n$$$, $$$u_i\ne v_i$$$), describing an undirected edge $$$(u_i,v_i)$$$ in the graph. The $$$i$$$-th edge in the input has weight $$$i$$$.

It is guaranteed that the graph is connected and there is at most one edge between any pair of vertices.

Output

You need to output a binary string $$$s$$$, where $$$s_i=1$$$ if findMST(i) creates an MST, and $$$s_i = 0$$$ otherwise.

Note

Here is the graph given in the first example.

$\text{[math]}$

There is only one minimum spanning tree in this graph. A minimum spanning tree is $$$(1,2),(3,5),(1,3),(2,4)$$$ which has weight $$$1+2+3+5=11$$$.

Here is a part of the process of calling findMST(1):

reset the array vis and the edge set s;
calling dfs(1);
vis[1] := true;
iterate through each edge $$$(1,2),(1,3)$$$;
add edge $$$(1,2)$$$ into the edge set s, calling dfs(2):
- vis[2] := true
- iterate through each edge $$$(2,1),(2,3),(2,4)$$$;
- because vis[1] = true, ignore the edge $$$(2,1)$$$;
- add edge $$$(2,3)$$$ into the edge set s, calling dfs(3):
  - ...

In the end, it will select edges $$$(1,2),(2,3),(3,5),(2,4)$$$ with total weight $$$1+4+2+5=12 \gt 11$$$, so findMST(1) does not find a minimum spanning tree.

It can be shown that the other trees are all MSTs, so the answer is 01111.

DFS Trees

Examples