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 std::max;
using std::min;
const int inf = 0x3f3f3f3f, Inf = 0x7fffffff;
const long long INF = 0x3f3f3f3f3f3f3f3f;
__inline__ __attribute__((always_inline)) unsigned int rnd() {
  static unsigned int seed = 416;
  return seed += 0x71dad4bfu, seed ^= seed >> 5, seed += 0xc6f74d88u,
         seed ^= seed << 17, seed += 0x25e6561u, seed ^= seed >> 13;
}
template <typename _Tp>
_Tp gcd(const _Tp &a, const _Tp &b) {
  return (!b) ? a : gcd(b, a % b);
}
template <typename _Tp>
__inline__ __attribute__((always_inline)) _Tp abs(const _Tp &a) {
  return a >= 0 ? a : -a;
}
template <typename _Tp>
__inline__ __attribute__((always_inline)) void chmax(_Tp &a, const _Tp &b) {
  (a < b) && (a = b);
}
template <typename _Tp>
__inline__ __attribute__((always_inline)) void chmin(_Tp &a, const _Tp &b) {
  (b < a) && (a = b);
}
template <typename _Tp>
__inline__ __attribute__((always_inline)) void read(_Tp &x) {
  char ch(getchar());
  bool f(false);
  while (!isdigit(ch)) f |= ch == 45, ch = getchar();
  x = ch & 15, ch = getchar();
  while (isdigit(ch)) x = (((x << 2) + x) << 1) + (ch & 15), ch = getchar();
  f && (x = -x);
}
template <typename _Tp, typename... Args>
__inline__ __attribute__((always_inline)) void read(_Tp &t, Args &...args) {
  read(t);
  read(args...);
}
template <typename _Tp, typename... Args>
__inline__ __attribute__((always_inline)) _Tp min(const _Tp &a, const _Tp &b,
                                                  const Args &...args) {
  return a < b ? min(a, args...) : min(b, args...);
}
template <typename _Tp, typename... Args>
__inline__ __attribute__((always_inline)) _Tp max(const _Tp &a, const _Tp &b,
                                                  const Args &...args) {
  return a < b ? max(b, args...) : max(a, args...);
}
__inline__ __attribute__((always_inline)) int read_str(char *s) {
  char ch(getchar());
  while (ch == ' ' || ch == '\r' || ch == '\n') ch = getchar();
  char *tar = s;
  *tar = ch, ch = getchar();
  while (ch != ' ' && ch != '\r' && ch != '\n' && ch != EOF)
    *(++tar) = ch, ch = getchar();
  return tar - s + 1;
}
const int N = 615;
namespace flow {
struct edge {
  int v, nxt;
  int w;
} c[N * N << 4];
int front[N], edge_cnt;
int cur[N], dep[N], S, T;
int _q[N], _l, _r;
int node_cnt;
__inline__ __attribute__((always_inline)) void addedge(int u, int v, int w) {
  c[++edge_cnt] = (edge){v, front[u], w}, front[u] = edge_cnt;
  c[++edge_cnt] = (edge){u, front[v], 0}, front[v] = edge_cnt;
}
__inline__ __attribute__((always_inline)) void init() {
  memset(front, 255, sizeof(front)), edge_cnt = -1;
}
bool bfs() {
  memset(dep, 255, (node_cnt + 3) << 2);
  memcpy(cur, front, (node_cnt + 3) << 2);
  dep[S] = 0;
  _q[_l = _r = 1] = S;
  while (_l != _r + 1) {
    int x = _q[_l++];
    for (int i = front[x]; ~i; i = c[i].nxt) {
      if (c[i].w && !~dep[c[i].v]) {
        dep[c[i].v] = dep[x] + 1;
        _q[++_r] = c[i].v;
      }
    }
  }
  return ~dep[T];
}
int dfs(int x, int flow) {
  if (x == T || !flow) return flow;
  int f = 0, rf;
  for (int &i = cur[x]; ~i; i = c[i].nxt) {
    if (dep[c[i].v] == dep[x] + 1 && (rf = dfs(c[i].v, min(flow, c[i].w)))) {
      flow -= rf, f += rf;
      c[i].w -= rf, c[i ^ 1].w += rf;
      if (!flow) return f;
    }
  }
  return f;
}
int dinic() {
  int ans = 0;
  while (bfs()) ans += dfs(S, inf);
  return ans;
}
}  // namespace flow
using namespace flow;
int get() {
  static char s[15];
  int len = read_str(s);
  if (s[0] == '?') return -1;
  int x = 0;
  for (int i = 0; i < len; ++i) x = x * 10 + s[i] - 48;
  return x;
}
int D[N], L[N];
int d[N], l[N];
int maxx[N], cnt[N];
bool vis[N][N];
std::vector<int> nd[N][N];
int to[N], n;
int pre[N], id;
int _d_[N], _l_[N];
void solve() {
  memset(_d_, 0, sizeof(_d_));
  memset(_l_, 0, sizeof(_l_));
  memcpy(d, D, sizeof(d));
  memcpy(l, L, sizeof(l));
  memset(maxx, -1, sizeof(maxx));
  memset(vis, 0, sizeof(vis));
  memset(cnt, 0, sizeof(cnt));
  memset(pre, 0, sizeof(pre));
  init();
  for (int i = 1; i <= n; ++i) {
    if (~d[i] && ~l[i]) {
      chmax(maxx[l[i]], d[i]);
      if (d[i] == 0) ++cnt[l[i]];
      vis[l[i]][d[i]] = true;
    }
    if (~l[i]) chmax(maxx[l[i]], 0);
  }
  int qwq = 0;
  for (int i = 1; i <= n; ++i)
    if (~maxx[i]) qwq += maxx[i] + i;
  if (qwq > n) return;
  int sum = 0;
  for (int i = 1; i <= n; ++i) {
    if (~maxx[i]) {
      ++pre[0];
      _d_[pre[0]] = 0, _l_[pre[0]] = i;
      int rest = i - cnt[i] % i;
      if (rest == i && cnt[i]) continue;
      addedge(pre[0] + n, T, rest);
      sum += rest;
      for (int j = 1; j <= n; ++j) {
        if (~d[j] && ~l[j]) continue;
        if ((d[j] == -1 || d[j] == 0) && (l[j] == -1 || l[j] == i))
          addedge(j, pre[0] + n, 1);
      }
    }
  }
  for (int i = 1; i <= n; ++i) {
    pre[i] = pre[i - 1];
    if (~maxx[i]) {
      for (int j = 1; j < maxx[i]; ++j) {
        if (!vis[i][j]) {
          _d_[pre[i] + j] = j, _l_[pre[i] + j] = i;
          addedge(n + pre[i] + j, T, 1);
          ++sum;
          for (int k = 1; k <= n; ++k) {
            if (~d[k] && ~l[k]) continue;
            if ((d[k] == j || d[k] == -1) && (l[k] == i || l[k] == -1))
              addedge(k, n + pre[i] + j, 1);
          }
        }
      }
      if (maxx[i]) pre[i] += maxx[i] - 1;
    }
  }
  for (int i = 1; i <= n; ++i)
    if (d[i] == -1 || l[i] == -1) addedge(S, i, 1);
  int ans = dinic();
  if (ans != sum) return;
  for (int i = 1; i <= n; ++i) {
    if (~d[i] && ~l[i]) continue;
    for (int _ = front[i]; ~_; _ = c[_].nxt) {
      int v = c[_].v, w = c[_].w;
      if (!w && v != S) d[i] = _d_[v - n], l[i] = _l_[v - n];
    }
    if (d[i] == -1 && l[i] == -1)
      d[i] = 0, l[i] = 1;
    else if (d[i] == -1) {
      if (l[i] == 1)
        d[i] = 0;
      else
        d[i] = 1;
    } else if (l[i] == -1) {
      if (d[i] == 0)
        l[i] = 1;
      else
        l[i] = l[id];
    }
  }
  for (int i = 1; i <= n; ++i) nd[l[i]][d[i]].push_back(i);
  for (int i = 1; i <= n; ++i) {
    assert(((int)nd[i][0].size()) % i == 0);
    for (int l = 0, r = i; r <= ((int)nd[i][0].size()); l += i, r += i) {
      int last = nd[i][0][r - 1];
      for (int j = l; j < r; ++j) {
        to[nd[i][0][j]] = last;
        last = nd[i][0][j];
      }
    }
    for (int j = 1; j <= n; ++j) {
      if (nd[i][j].empty()) break;
      for (auto it : nd[i][j]) to[it] = nd[i][j - 1].back();
    }
  }
  for (int i = 1; i <= n; ++i) printf("%d%c", to[i], " \n"[i == n]);
  exit(0);
}
int main() {
  read(n);
  S = n + n + 1, T = S + 1, node_cnt = T;
  for (int i = 1; i <= n; ++i) D[i] = get(), L[i] = get();
  id = 1;
  for (int i = 2; i <= n; ++i)
    if (D[i] > D[id] || (D[i] == D[id] && L[i] != -1)) id = i;
  if (L[id] != -1)
    solve();
  else {
    for (int i = 1; i <= n; ++i) {
      L[id] = i;
      solve();
    }
  }
  puts("-1");
  return 0;
}