#include<cstdio>
#include<algorithm>
using namespace std;
const int N=200011;
template<typename TP>void read(TP &kk){
    #define ak *
    TP phy=0,ioi=1;char ch=getchar();
    while(ch<'0'||ch>'9'){if(ch=='-')ioi=-1;ch=getchar();}
    while(ch>='0'&&ch<='9'){phy=phy*10+ch-'0';ch=getchar();}
    kk=phy ak ioi;
}
int n;
struct sumireko
{
    int to,ne;
}e[N*2];
int he[N],ecnt;
void addline(int f,int t)
{
    e[++ecnt].to=t;
    e[ecnt].ne=he[f];
    he[f]=ecnt;
}
int fa[N];
int rnd[N],hp;
bool vv[N],onr[N];
int sp;
int ip[N],iar;
void find()
{
    int x=1;
    while(!vv[x]) vv[x]=1,x=fa[x];
    while(!onr[x]) onr[x]=1,rnd[++hp]=x,x=fa[x];
}

int dp[N],g[N],tmp;
void dfs(int x)
{
    for(int i=he[x],t;i;i=e[i].ne)
    {
        t=e[i].to;
        if(!onr[t]) dfs(t);
    }
    tmp++;
    for(int i=he[x],t;i;i=e[i].ne)
    {
        t=e[i].to;
        if(!onr[t]) g[dp[t]]=tmp;
    }
    dp[x]=0;
    while(g[dp[x]]==tmp) dp[x]++;
}

int ma=-1,mi=19260817;
int xi,yi,wi;
int main()
{
    read(n);
    for(int i=1;i<=n;i++)
    {
        read(fa[i]);
        addline(fa[i],i);
    }
    find();
    if(hp&1)
    {
        for(int i=1;i<=hp;i++)
        {
            int x=rnd[i];
            dfs(x);
            ma=max(ma,dp[x]),mi=min(mi,dp[x]);
        }
        if(ma==mi) puts("IMPOSSIBLE");
        else puts("POSSIBLE");
    }else puts("POSSIBLE");
    return 0;
}
### Prompt

Please formulate a cpp solution to the following problem:

There is a directed graph with N vertices and N edges. The vertices are numbered 1, 2, ..., N.

The graph has the following N edges: (p_1, 1), (p_2, 2), ..., (p_N, N), and the graph is weakly connected. Here, an edge from Vertex u to Vertex v is denoted by (u, v), and a weakly connected graph is a graph which would be connected if each edge was bidirectional.

We would like to assign a value to each of the vertices in this graph so that the following conditions are satisfied. Here, a_i is the value assigned to Vertex i.

* Each a_i is a non-negative integer.
* For each edge (i, j), a_i \neq a_j holds.
* For each i and each integer x(0 ≤ x < a_i), there exists a vertex j such that the edge (i, j) exists and x = a_j holds.



Determine whether there exists such an assignment.

Constraints

* 2 ≤ N ≤ 200 000
* 1 ≤ p_i ≤ N
* p_i \neq i
* The graph is weakly connected.

Input

Input is given from Standard Input in the following format:


N
p_1 p_2 ... p_N


Output

If the assignment is possible, print `POSSIBLE`; otherwise, print `IMPOSSIBLE`.

Examples

Input

4
2 3 4 1


Output

POSSIBLE


Input

3
2 3 1


Output

IMPOSSIBLE


Input

4
2 3 1 1


Output

POSSIBLE


Input

6
4 5 6 5 6 4


Output

IMPOSSIBLE

### Response

```cpp
#include<cstdio>
#include<algorithm>
using namespace std;
const int N=200011;
template<typename TP>void read(TP &kk){
    #define ak *
    TP phy=0,ioi=1;char ch=getchar();
    while(ch<'0'||ch>'9'){if(ch=='-')ioi=-1;ch=getchar();}
    while(ch>='0'&&ch<='9'){phy=phy*10+ch-'0';ch=getchar();}
    kk=phy ak ioi;
}
int n;
struct sumireko
{
    int to,ne;
}e[N*2];
int he[N],ecnt;
void addline(int f,int t)
{
    e[++ecnt].to=t;
    e[ecnt].ne=he[f];
    he[f]=ecnt;
}
int fa[N];
int rnd[N],hp;
bool vv[N],onr[N];
int sp;
int ip[N],iar;
void find()
{
    int x=1;
    while(!vv[x]) vv[x]=1,x=fa[x];
    while(!onr[x]) onr[x]=1,rnd[++hp]=x,x=fa[x];
}

int dp[N],g[N],tmp;
void dfs(int x)
{
    for(int i=he[x],t;i;i=e[i].ne)
    {
        t=e[i].to;
        if(!onr[t]) dfs(t);
    }
    tmp++;
    for(int i=he[x],t;i;i=e[i].ne)
    {
        t=e[i].to;
        if(!onr[t]) g[dp[t]]=tmp;
    }
    dp[x]=0;
    while(g[dp[x]]==tmp) dp[x]++;
}

int ma=-1,mi=19260817;
int xi,yi,wi;
int main()
{
    read(n);
    for(int i=1;i<=n;i++)
    {
        read(fa[i]);
        addline(fa[i],i);
    }
    find();
    if(hp&1)
    {
        for(int i=1;i<=hp;i++)
        {
            int x=rnd[i];
            dfs(x);
            ma=max(ma,dp[x]),mi=min(mi,dp[x]);
        }
        if(ma==mi) puts("IMPOSSIBLE");
        else puts("POSSIBLE");
    }else puts("POSSIBLE");
    return 0;
}
```