Problem: A balancing network is an abstract device built up of N wires, thought of as running from left to right, and M balancers that connect pairs of wires. The wires are numbered from 1 to N from top to bottom, and the balancers are numbered from 1 to M from left to right. Balancer i connects wires x_i and y_i (x_i < y_i).

pic1-small-2acea94b.png

Each balancer must be in one of two states: up or down.

Consider a token that starts moving to the right along some wire at a point to the left of all balancers. During the process, the token passes through each balancer exactly once. Whenever the token encounters balancer i, the following happens:

* If the token is moving along wire x_i and balancer i is in the down state, the token moves down to wire y_i and continues moving to the right.
* If the token is moving along wire y_i and balancer i is in the up state, the token moves up to wire x_i and continues moving to the right.
* Otherwise, the token doesn't change the wire it's moving along.



Let a state of the balancing network be a string of length M, describing the states of all balancers. The i-th character is `^` if balancer i is in the up state, and `v` if balancer i is in the down state.

A state of the balancing network is called uniforming if a wire w exists such that, regardless of the starting wire, the token will always end up at wire w and run to infinity along it. Any other state is called non-uniforming.

You are given an integer T (1 \le T \le 2). Answer the following question:

* If T = 1, find any uniforming state of the network or determine that it doesn't exist.
* If T = 2, find any non-uniforming state of the network or determine that it doesn't exist.



Note that if you answer just one kind of questions correctly, you can get partial score.

Constraints

* 2 \leq N \leq 50000
* 1 \leq M \leq 100000
* 1 \leq T \leq 2
* 1 \leq x_i < y_i \leq N
* All input values are integers.

Input

Input is given from Standard Input in the following format:


N M T
x_1 y_1
x_2 y_2
:
x_M y_M


Output

Print any uniforming state of the given network if T = 1, or any non-uniforming state if T = 2. If the required state doesn't exist, output `-1`.

Examples

Input

4 5 1
1 3
2 4
1 2
3 4
2 3


Output

^^^^^


Input

4 5 2
1 3
2 4
1 2
3 4
2 3


Output

v^^^^


Input

3 1 1
1 2


Output

-1


Input

2 1 2
1 2


Output

-1

Solution (in CPP):

Solution:
#include<bits/stdc++.h>
#define Tp template<typename Ty>
#define Ts template<typename Ty,typename... Ar>
#define Reg register
#define RI Reg int
#define Con const
#define CI Con int&
#define I inline
#define W while
#define N 50000
#define M 100000
using namespace std;
int n,m,op,a[M+5],b[M+5];char ans[M+5];
class UniformingSolver
{
	private:
		int p[N+5];bitset<N+5> S[N+5];
	public:
		I void Solve()
		{
			RI i,j;for(i=1;i<=n;++i) S[i].set(i);
			for(i=1;i<=m;++i) S[a[i]]=S[b[i]]=S[a[i]]|S[b[i]];
			for(i=1;i<=n;++i) if(S[i].count()==n)
			{
				for(p[i]=1,j=m;j;--j) p[a[j]]?
					(p[b[j]]=1,ans[j]='^'):(p[a[j]]=p[b[j]],ans[j]='v');
				puts(ans+1);return;
			}puts("-1");
		}
}S1;
class NonUniformingSolver
{
	private:
		int t[N+5],k[N+5];
	public:
		I void Solve()
		{
			RI i;if(n<=2) return (void)(puts("-1"));for(i=1;i<=n;++i) k[t[i]=i]=1;
			#define U(x,y) (--k[t[x]],++k[t[x]=t[y]])
			for(i=m;i;--i) k[t[a[i]]]<=k[t[b[i]]]?
				(ans[i]='^',U(b[i],a[i])):(ans[i]='v',U(a[i],b[i]));
			puts(ans+1);
		}
}S2;
int main()
{
	RI i;for(scanf("%d%d%d",&n,&m,&op),i=1;i<=m;++i) scanf("%d%d",a+i,b+i);
	return op==1?S1.Solve():S2.Solve(),0;
}