#include <bits/stdc++.h>
#define rep(i, x, y) for (int i = x; i <= y; i++)
using namespace std;

typedef long long ll;
const int N = 2e5 + 10;
ll n, fa[N], sg[N], num, mx = -1e18, mn = 1e18;
bool vis[N], onc[N], h[N];
vector<int> g[N];

void dfs(int x) {
    for (int i = 0; i < g[x].size(); i++) {
        int y = g[x][i];
        if (onc[y]) continue;
        dfs(y);
    }
    for (int i = 0; i < g[x].size(); i++) {
        int y = g[x][i];
        if (onc[y]) continue;
        h[sg[y]] = 1;
    }
    for (; h[sg[x]]; ++sg[x]);
    for (int i = 0; i < g[x].size(); i++) {
        int y = g[x][i];
        if (onc[y]) continue;
        h[sg[y]] = 0;
    }
}

int main() {
    cin >> n;
    rep(i, 1, n) scanf("%lld", &fa[i]), g[fa[i]].push_back(i);
    int cur = 1;
    for (; !vis[cur]; cur = fa[cur]) vis[cur] = 1;
    for (; !onc[cur]; cur = fa[cur]) onc[cur] = 1;
    rep(i, 1, n) if (onc[i]) {
        dfs(i);
        ++num; mx = max(mx, sg[i]), mn = min(mn, sg[i]);
    }
    puts((num & 1) && mx == mn ? "IMPOSSIBLE" : "POSSIBLE");
    return 0;
}
### Prompt

Please create a solution in Cpp 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 <bits/stdc++.h>
#define rep(i, x, y) for (int i = x; i <= y; i++)
using namespace std;

typedef long long ll;
const int N = 2e5 + 10;
ll n, fa[N], sg[N], num, mx = -1e18, mn = 1e18;
bool vis[N], onc[N], h[N];
vector<int> g[N];

void dfs(int x) {
    for (int i = 0; i < g[x].size(); i++) {
        int y = g[x][i];
        if (onc[y]) continue;
        dfs(y);
    }
    for (int i = 0; i < g[x].size(); i++) {
        int y = g[x][i];
        if (onc[y]) continue;
        h[sg[y]] = 1;
    }
    for (; h[sg[x]]; ++sg[x]);
    for (int i = 0; i < g[x].size(); i++) {
        int y = g[x][i];
        if (onc[y]) continue;
        h[sg[y]] = 0;
    }
}

int main() {
    cin >> n;
    rep(i, 1, n) scanf("%lld", &fa[i]), g[fa[i]].push_back(i);
    int cur = 1;
    for (; !vis[cur]; cur = fa[cur]) vis[cur] = 1;
    for (; !onc[cur]; cur = fa[cur]) onc[cur] = 1;
    rep(i, 1, n) if (onc[i]) {
        dfs(i);
        ++num; mx = max(mx, sg[i]), mn = min(mn, sg[i]);
    }
    puts((num & 1) && mx == mn ? "IMPOSSIBLE" : "POSSIBLE");
    return 0;
}
```