Problem: Functional graph is a directed graph in which all vertices have outdegree equal to 1. Loops are allowed.

Some vertices of a functional graph lay on a cycle. From the others we can come to a cycle by making a finite number of steps along the edges (we consider only finite functional graphs in this problem).

Let's compute two values for each vertex. precyclei is the amount of edges we should pass to get to a vertex which is a part of some cycle (zero, if i itself lies on a cycle), cyclei is the length of the cycle we get to.

You are given the information about these values for some functional graph. For each vertex you know the values precyclei and cyclei, however, instead of some values there can be the question mark. It means that these values are unknown.

Build any functional graph that suits the description or determine that there is no such graph.

Input

The first line contains single integer n (1 ≤ n ≤ 300) — the number of vertices in the graph.

Each of the next n lines contain two integers — precyclei (0 ≤ precyclei ≤ n - 1) and cyclei (1 ≤ cyclei ≤ n). There could be question marks instead of some of these values.

Output

In case there is no solution, print -1.

Otherwise, print n integers. i-th of them is the number of vertex to which the edge form the i-th vertex go.

The vertices should be in the same order as they go in input data.

If there are multiple solutions, print any of them.

Examples

Input

3
0 3
0 3
? ?


Output

2 3 1 


Input

5
3 2
? ?
? ?
? ?
? ?


Output

5 3 2 2 4 


Input

8
? 3
? ?
0 2
0 2
0 3
0 3
0 3
3 3


Output

5 1 4 3 6 7 5 2 


Input

1
? ?


Output

1 


Input

6
0 3
0 3
0 3
0 3
0 3
0 3


Output

2 3 1 5 6 4 


Input

2
1 1
1 1


Output

-1

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
const int N = 333;
const long long INF = 1e9 + 19;
struct Node {
  int pre, cyc;
  Node() {}
  Node(int _pre, int _cyc) : pre(_pre), cyc(_cyc) {}
};
int n;
Node a[N];
Node aa[N];
vector<int> e[N];
int p[N];
bool use[N];
bool superUse[N];
int answer[N];
int who[N][N];
int dfs(int v) {
  use[v] = 1;
  for (auto u : e[v]) {
    if (p[u] == -1 || (!use[p[u]] && dfs(p[u]))) {
      p[u] = v;
      return 1;
    }
  }
  return 0;
}
void read() {
  scanf("%d", &n);
  for (int i = 0; i < n; i++) {
    string s1, s2;
    cin >> s1 >> s2;
    int x, y;
    if (s1 == "?") {
      x = -1;
    } else {
      stringstream ss;
      ss << s1;
      ss >> x;
    }
    if (s2 == "?") {
      y = -1;
    } else {
      stringstream ss;
      ss << s2;
      ss >> y;
    }
    a[i] = Node(x, y);
  }
  for (int i = 0; i < n; i++) aa[i] = a[i];
}
bool match(Node cand, Node need) {
  return (cand.pre == -1 || cand.pre == need.pre) &&
         (cand.cyc == -1 || cand.cyc == need.cyc);
}
bool valid() {
  for (int i = 0; i < n; i++) {
    assert(match(aa[i], a[i]));
  }
  for (int i = 0; i < n; i++) {
    map<int, int> vis;
    int v = i;
    for (int tmr = 0;; tmr++) {
      if (vis.count(v) == 1) {
        int cyc = tmr - vis[v];
        int pre = vis[v];
        if (!(cyc == a[i].cyc && pre == a[i].pre)) return 0;
        break;
      }
      vis[v] = tmr;
      v = answer[v];
    }
  }
  return 1;
}
bool build() {
  memset(who, -1, sizeof(who));
  memset(answer, -1, sizeof(answer));
  for (int len = 1; len <= n; len++) {
    vector<int> tmp;
    for (int i = 0; i < n; i++)
      if (a[i].pre == 0 && a[i].cyc == len) {
        tmp.push_back(i);
      }
    if (tmp.size() % len != 0) return 0;
    for (int i = 0; i < (int)tmp.size(); i++) {
      answer[tmp[i]] = tmp[i - i % len + (i + 1) % len];
    }
  }
  for (int i = 0; i < n; i++) who[a[i].pre][a[i].cyc] = i;
  for (int i = 0; i < n; i++)
    if (a[i].pre != 0) {
      answer[i] = who[a[i].pre - 1][a[i].cyc];
    }
  return valid();
}
vector<int> solve() {
  int pp = 0;
  for (int i = 0; i < n; i++) pp = max(pp, a[i].pre);
  bool cool = 0;
  for (int whoMax = 1; whoMax <= n; whoMax++) {
    for (int i = 0; i < n; i++) a[i] = aa[i];
    for (int i = 0; i < n; i++) e[i].clear();
    memset(superUse, 0, sizeof(superUse));
    bool allQCyc = 1;
    for (int i = 0; i < n; i++) {
      allQCyc &= a[i].cyc == -1;
    }
    if (allQCyc) {
      a[0].cyc = 1;
    }
    vector<Node> need;
    vector<int> mxPre(n + 1);
    for (int len = 1; len <= n; len++) {
      vector<int> cnt(n);
      int mx = -1;
      for (int i = 0; i < n; i++)
        if (a[i].cyc == len) {
          if (a[i].pre != -1)
            cnt[a[i].pre]++;
          else
            mx = 0;
        }
      for (int i = 0; i < n; i++)
        if (cnt[i] > 0) mx = i;
      if (len == whoMax) mx = pp;
      mxPre[len] = mx;
      if (mx != -1) {
        for (int i = 1; i <= mx; i++)
          if (cnt[i] == 0) need.push_back(Node(i, len));
        int needZero;
        if (cnt[0] == 0)
          needZero = len;
        else {
          needZero = (len - cnt[0] % len) % len;
        }
        for (int i = 0; i < needZero; i++) need.push_back(Node(0, len));
      }
    }
    if ((int)need.size() > n) {
      continue;
    }
    for (int i = 0; i < n; i++) {
      if ((a[i].pre == -1) != (a[i].cyc == -1)) {
        for (int j = 0; j < (int)need.size(); j++)
          if (match(a[i], need[j])) {
            e[i].push_back(j);
          }
      }
    }
    for (int i = 0; i < (int)need.size(); i++) p[i] = -1;
    vector<int> perm;
    for (int i = 0; i < n; i++)
      if ((a[i].pre == -1) != (a[i].cyc == -1)) perm.push_back(i);
    for (int i = 0; i < n; i++) {
      memset(use, 0, sizeof(use));
      superUse[i] = dfs(i);
    }
    bool fail = 0;
    for (int i = 0; i < (int)need.size(); i++) {
      if (p[i] == -1) {
        bool good = 0;
        for (int j = 0; j < n; j++)
          if (a[j].pre == -1 && a[j].cyc == -1 && superUse[j] == 0) {
            superUse[j] = 1;
            p[i] = j;
            good = 1;
            break;
          }
        if (!good) {
          fail = 1;
          break;
        }
      }
      assert(match(a[p[i]], need[i]));
      a[p[i]] = need[i];
    }
    if (fail) continue;
    for (int i = 0; i < n; i++) {
      if (!superUse[i] && a[i].cyc == -1 && a[i].pre == 0) {
        a[i].cyc = 1;
      }
    }
    for (int i = 0; i < n; i++) {
      if (!superUse[i] && a[i].pre == -1 && a[i].cyc != -1) {
        int len = a[i].cyc;
        superUse[i] = 1;
        mxPre[len]++;
        a[i].pre = mxPre[len];
      }
    }
    int longestPre = -1;
    for (int len = 1; len <= n; len++) {
      if (mxPre[len] >= 0 &&
          (longestPre == -1 || mxPre[len] > mxPre[longestPre])) {
        longestPre = len;
      }
    }
    assert(longestPre != -1);
    for (int i = mxPre[longestPre] + 1; i <= n; i++) {
      int whoCan = -1;
      for (int j = 0; j < n; j++) {
        if (superUse[j] == 0 && a[j].pre == i && a[j].cyc == -1) {
          whoCan = j;
          break;
        }
      }
      if (whoCan != -1) {
        superUse[whoCan] = 1;
        a[whoCan].cyc = longestPre;
      } else {
        bool ok = 0;
        for (int j = 0; j < n; j++) {
          if (superUse[j] == 0 && a[j].pre == -1 && a[j].cyc == -1) {
            superUse[j] = 1;
            a[j] = Node(i, longestPre);
            ok = 1;
            break;
          }
        }
        if (!ok) break;
      }
      mxPre[longestPre]++;
    }
    for (int i = 0; i < n; i++) {
      if (a[i].cyc == -1 && a[i].pre > mxPre[longestPre]) {
        assert(false);
        return vector<int>();
      }
    }
    for (int i = 0; i < n; i++)
      if (a[i].cyc == -1) {
        a[i].cyc = longestPre;
      }
    if (build()) {
      cool = 1;
      break;
    }
  }
  if (cool) {
    vector<int> tmp;
    for (int i = 0; i < n; i++) tmp.push_back(answer[i]);
    return tmp;
  }
  return vector<int>();
}
void printTest() {
  cout << n << endl;
  for (int i = 0; i < n; i++) {
    if (aa[i].pre == -1)
      cout << "?";
    else
      cout << aa[i].pre;
    cout << " ";
    if (aa[i].cyc == -1)
      cout << "?";
    else
      cout << aa[i].cyc;
    cout << endl;
  }
}
void genTest() {
  n = rand() % 6 + 1;
  for (int i = 0; i < n; i++) {
    int pre = rand() % (n + 1) - 1;
    int cyc = rand() % (n + 1) - 1;
    if (cyc == 0) cyc++;
    aa[i] = a[i] = Node(pre, cyc);
  }
}
struct A {
  int l, r;
  int id, type;
};
vector<A> forRec;
vector<int> hh;
int val[N * 2];
bool valid2() {
  for (int i = 0; i < n; i++)
    if (answer[i] == -1) return 0;
  for (int i = 0; i < n; i++) {
    assert(match(aa[i], a[i]));
  }
  for (int i = 0; i < n; i++) {
    map<int, int> vis;
    int v = i;
    for (int tmr = 0;; tmr++) {
      if (vis.count(v) == 1) {
        int cyc = tmr - vis[v];
        int pre = vis[v];
        if (!(cyc == a[i].cyc && pre == a[i].pre)) return 0;
        break;
      }
      vis[v] = tmr;
      v = answer[v];
    }
  }
  return 1;
}
bool build2() {
  memset(who, -1, sizeof(who));
  memset(answer, -1, sizeof(answer));
  for (int len = 1; len <= n; len++) {
    vector<int> tmp;
    for (int i = 0; i < n; i++)
      if (a[i].pre == 0 && a[i].cyc == len) {
        tmp.push_back(i);
      }
    if (tmp.size() % len != 0) return 0;
    assert(tmp.size() % len == 0);
    for (int i = 0; i < (int)tmp.size(); i++) {
      answer[tmp[i]] = tmp[i - i % len + (i + 1) % len];
    }
  }
  for (int i = 0; i < n; i++) who[a[i].pre][a[i].cyc] = i;
  for (int i = 0; i < n; i++)
    if (a[i].pre != 0) {
      answer[i] = who[a[i].pre - 1][a[i].cyc];
    }
  return valid2();
}
void rec(int pos) {
  if (!hh.empty()) return;
  if (pos == (int)forRec.size()) {
    for (int i = 0; i < n; i++) a[i] = aa[i];
    for (int i = 0; i < (int)forRec.size(); i++) {
      if (forRec[i].type == 0)
        a[forRec[i].id].pre = val[i];
      else
        a[forRec[i].id].cyc = val[i];
    }
    if (build2()) {
      hh.clear();
      for (int i = 0; i < n; i++) hh.push_back(answer[i]);
    }
    return;
  }
  for (int i = forRec[pos].l; i <= forRec[pos].r; i++) {
    val[pos] = i;
    rec(pos + 1);
  }
}
vector<int> stupid() {
  forRec.clear();
  for (int i = 0; i < n; i++) {
    if (aa[i].pre == -1) {
      forRec.push_back({0, n - 1, i, 0});
    }
    if (aa[i].cyc == -1) {
      forRec.push_back({1, n, i, 1});
    }
  }
  hh.clear();
  rec(0);
  return hh;
}
void stress() {
  for (int tt = 1334;; tt++) {
    srand(tt);
    cerr << "tt"
         << " = " << tt << endl;
    genTest();
    auto r1 = solve();
    auto r2 = stupid();
    cerr << "("
         << "r1.size()"
         << ", "
         << "r2.size()"
         << ") = (" << r1.size() << ", " << r2.size() << ")\n";
    ;
    if (r1.empty() != r2.empty()) {
      printTest();
    }
    assert(r1.size() == r2.size());
  }
}
void printAns(vector<int> A) {
  if (A.empty()) {
    puts("-1");
  } else {
    for (int i = 0; i < n; i++) {
      printf("%d ", A[i] + 1);
    }
    puts("");
  }
}
int main() {
  if (1) {
    read();
    printAns(solve());
  } else {
    stress();
  }
  return 0;
}