#include <bits/stdc++.h>
using namespace std;
const int N = 200010;
int _w;
struct SAM {
  int ch[N][26];
  int len[N];
  int pa[N];
  int idx;
  void init() {
    memset(ch, 0, sizeof ch);
    memset(len, 0, sizeof len);
    memset(pa, 0, sizeof pa);
    idx = 1;
    pa[0] = -1;
  }
  int append(int p, int c) {
    int np = idx++;
    len[np] = len[p] + 1;
    while (p != -1 && !ch[p][c]) ch[p][c] = np, p = pa[p];
    if (p == -1)
      pa[np] = 0;
    else {
      int q = ch[p][c];
      if (len[q] == len[p] + 1)
        pa[np] = q;
      else {
        int nq = idx++;
        memcpy(ch[nq], ch[q], sizeof ch[nq]);
        len[nq] = len[p] + 1;
        pa[nq] = pa[q];
        pa[q] = pa[np] = nq;
        while (p != -1 && ch[p][c] == q) ch[p][c] = nq, p = pa[p];
      }
    }
    return np;
  }
};
int n;
char str[N];
SAM sam, rsam;
long long solve_origin() {
  sam.init();
  int last = 0;
  for (int i = 1; i <= n; ++i) last = sam.append(last, str[i] - 'a');
  long long ans = 0;
  for (int i = 1; i < sam.idx; ++i) ans += sam.len[i] - sam.len[sam.pa[i]];
  return ans;
}
long long solve_before() {
  sam.init();
  int last = 0;
  for (int i = 2; i <= n; ++i) last = sam.append(last, str[i] - 'a');
  long long ans = 0;
  for (int i = 1; i < sam.idx; ++i) ans += sam.len[i] - sam.len[sam.pa[i]];
  return ans;
}
long long solve_after() {
  sam.init();
  int last = 0;
  for (int i = 1; i <= n - 1; ++i) last = sam.append(last, str[i] - 'a');
  long long ans = 0;
  for (int i = 1; i < sam.idx; ++i) ans += sam.len[i] - sam.len[sam.pa[i]];
  return ans;
}
struct Graph {
  int head[N], nxt[N], to[N], eid;
  void init() {
    eid = 0;
    memset(head, -1, sizeof head);
  }
  void link(int u, int v) { to[eid] = v, nxt[eid] = head[u], head[u] = eid++; }
};
Graph g, rg;
namespace HLD {
int dfn[N], dfnc, top[N], dep[N];
int pa[N], sz[N], son[N], val[N];
int rdfn[N];
void dfs1(int u, int fa, int d) {
  sz[u] = 1, dep[u] = d, pa[u] = fa;
  val[u] = rsam.len[u];
  for (int i = rg.head[u]; ~i; i = rg.nxt[i]) {
    int v = rg.to[i];
    dfs1(v, u, d + 1);
    sz[u] += sz[v];
    if (son[u] == -1 || sz[v] > sz[son[u]]) son[u] = v;
  }
}
void dfs2(int u, int tp) {
  dfn[u] = ++dfnc, top[u] = tp;
  rdfn[dfnc] = u;
  if (son[u] != -1) dfs2(son[u], tp);
  for (int i = rg.head[u]; ~i; i = rg.nxt[i]) {
    int v = rg.to[i];
    if (v != son[u]) dfs2(v, v);
  }
}
void init() {
  memset(son, -1, sizeof son);
  dfs1(0, -1, 1);
  dfs2(0, 0);
}
int lca(int u, int v) {
  while (top[u] != top[v]) {
    if (dep[top[u]] < dep[top[v]]) swap(u, v);
    u = pa[top[u]];
  }
  return dep[u] < dep[v] ? u : v;
}
}  // namespace HLD
int mark[N], rmark[N], rmark2nod[N];
long long solve_ans = 0, now = 0;
set<int> st;
void ins_node(int u) {
  u = mark[u];
  if (!u) return;
  u = rmark2nod[u + 2];
  u = HLD::dfn[u];
  if (st.empty()) {
    st.insert(u);
    u = HLD::rdfn[u];
    now += HLD::val[u];
  } else {
    auto after = st.lower_bound(u);
    auto before = after;
    --before;
    if (after == st.end()) {
      int L = *before;
      L = HLD::rdfn[L];
      u = HLD::rdfn[u];
      int lca = HLD::lca(L, u);
      now -= HLD::val[lca];
      now += HLD::val[u];
      u = HLD::dfn[u];
      st.insert(u);
    } else if (after == st.begin()) {
      int R = *after;
      R = HLD::rdfn[R];
      u = HLD::rdfn[u];
      int lca = HLD::lca(R, u);
      now -= HLD::val[lca];
      now += HLD::val[u];
      u = HLD::dfn[u];
      st.insert(u);
    } else {
      int L = *before;
      int R = *after;
      L = HLD::rdfn[L];
      R = HLD::rdfn[R];
      now += HLD::val[HLD::lca(L, R)];
      u = HLD::rdfn[u];
      now -= HLD::val[HLD::lca(L, u)];
      now -= HLD::val[HLD::lca(R, u)];
      now += HLD::val[u];
      u = HLD::dfn[u];
      st.insert(u);
    }
  }
}
void ins_tree(int u) {
  ins_node(u);
  for (int i = g.head[u]; ~i; i = g.nxt[i]) ins_tree(g.to[i]);
}
int sz[N], son[N];
void init_sack(int u) {
  sz[u] = 1, son[u] = -1;
  for (int i = g.head[u]; ~i; i = g.nxt[i]) {
    int v = g.to[i];
    init_sack(v);
    sz[u] += sz[v];
    if (son[u] == -1 || sz[v] > sz[son[u]]) son[u] = v;
  }
}
void sack(int u, bool clr) {
  for (int i = g.head[u]; ~i; i = g.nxt[i])
    if (g.to[i] != son[u]) sack(g.to[i], true);
  if (son[u] != -1) sack(son[u], false);
  for (int i = g.head[u]; ~i; i = g.nxt[i])
    if (g.to[i] != son[u]) ins_tree(g.to[i]);
  ins_node(u);
  if (u) solve_ans += 1LL * now * (sam.len[u] - sam.len[sam.pa[u]]);
  if (clr) st.clear(), now = 0;
}
long long solve() {
  sam.init();
  int last = 0;
  for (int i = 1; i <= n - 2; ++i) last = sam.append(last, str[i] - 'a');
  g.init();
  for (int i = 1; i < sam.idx; ++i) g.link(sam.pa[i], i);
  last = 0;
  for (int i = 1; i <= n - 2; ++i) {
    last = sam.ch[last][str[i] - 'a'];
    mark[last] = i;
  }
  rsam.init();
  last = 0;
  for (int i = n; i >= 3; --i) last = rsam.append(last, str[i] - 'a');
  rg.init();
  for (int i = 1; i < rsam.idx; ++i) rg.link(rsam.pa[i], i);
  last = 0;
  for (int i = n; i >= 3; --i) {
    last = rsam.ch[last][str[i] - 'a'];
    rmark[last] = i;
    rmark2nod[i] = last;
  }
  HLD::init();
  init_sack(0);
  sack(0, false);
  return solve_ans;
}
int main() {
  _w = scanf("%s", str + 1);
  n = (int)strlen(str + 1);
  long long ans = 0;
  ans += solve_origin();
  if (n >= 2) {
    ans += solve_before();
    ans += solve_after();
  }
  if (n >= 3) {
    ans += solve();
  }
  printf("%lld\n", ans + 2);
  return 0;
}

### Prompt

Please formulate a CPP solution to the following problem:

Consider a string s of n lowercase English letters. Let t_i be the string obtained by replacing the i-th character of s with an asterisk character *. For example, when s = abc, we have t_1 = \tt{*bc}, t_2 = \tt{a*c}, and t_3 = \tt{ab*}.

Given a string s, count the number of distinct strings of lowercase English letters and asterisks that occur as a substring of at least one string in the set \\{s, t_1, …, t_n \}. The empty string should be counted.

Note that *'s are just characters and do not play any special role as in, for example, regex matching.

Input

The only line contains a string s of n lowercase English letters (1 ≤ n ≤ 10^5).

Output

Print a single integer — the number of distinct strings of s, t_1, …, t_n.

Example

Input


abc


Output


15

Note

For the sample case, the distinct substrings are (empty string), a, b, c, *, ab, a*, bc, b*, *b, *c, abc, ab*, a*c, *bc.

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
const int N = 200010;
int _w;
struct SAM {
  int ch[N][26];
  int len[N];
  int pa[N];
  int idx;
  void init() {
    memset(ch, 0, sizeof ch);
    memset(len, 0, sizeof len);
    memset(pa, 0, sizeof pa);
    idx = 1;
    pa[0] = -1;
  }
  int append(int p, int c) {
    int np = idx++;
    len[np] = len[p] + 1;
    while (p != -1 && !ch[p][c]) ch[p][c] = np, p = pa[p];
    if (p == -1)
      pa[np] = 0;
    else {
      int q = ch[p][c];
      if (len[q] == len[p] + 1)
        pa[np] = q;
      else {
        int nq = idx++;
        memcpy(ch[nq], ch[q], sizeof ch[nq]);
        len[nq] = len[p] + 1;
        pa[nq] = pa[q];
        pa[q] = pa[np] = nq;
        while (p != -1 && ch[p][c] == q) ch[p][c] = nq, p = pa[p];
      }
    }
    return np;
  }
};
int n;
char str[N];
SAM sam, rsam;
long long solve_origin() {
  sam.init();
  int last = 0;
  for (int i = 1; i <= n; ++i) last = sam.append(last, str[i] - 'a');
  long long ans = 0;
  for (int i = 1; i < sam.idx; ++i) ans += sam.len[i] - sam.len[sam.pa[i]];
  return ans;
}
long long solve_before() {
  sam.init();
  int last = 0;
  for (int i = 2; i <= n; ++i) last = sam.append(last, str[i] - 'a');
  long long ans = 0;
  for (int i = 1; i < sam.idx; ++i) ans += sam.len[i] - sam.len[sam.pa[i]];
  return ans;
}
long long solve_after() {
  sam.init();
  int last = 0;
  for (int i = 1; i <= n - 1; ++i) last = sam.append(last, str[i] - 'a');
  long long ans = 0;
  for (int i = 1; i < sam.idx; ++i) ans += sam.len[i] - sam.len[sam.pa[i]];
  return ans;
}
struct Graph {
  int head[N], nxt[N], to[N], eid;
  void init() {
    eid = 0;
    memset(head, -1, sizeof head);
  }
  void link(int u, int v) { to[eid] = v, nxt[eid] = head[u], head[u] = eid++; }
};
Graph g, rg;
namespace HLD {
int dfn[N], dfnc, top[N], dep[N];
int pa[N], sz[N], son[N], val[N];
int rdfn[N];
void dfs1(int u, int fa, int d) {
  sz[u] = 1, dep[u] = d, pa[u] = fa;
  val[u] = rsam.len[u];
  for (int i = rg.head[u]; ~i; i = rg.nxt[i]) {
    int v = rg.to[i];
    dfs1(v, u, d + 1);
    sz[u] += sz[v];
    if (son[u] == -1 || sz[v] > sz[son[u]]) son[u] = v;
  }
}
void dfs2(int u, int tp) {
  dfn[u] = ++dfnc, top[u] = tp;
  rdfn[dfnc] = u;
  if (son[u] != -1) dfs2(son[u], tp);
  for (int i = rg.head[u]; ~i; i = rg.nxt[i]) {
    int v = rg.to[i];
    if (v != son[u]) dfs2(v, v);
  }
}
void init() {
  memset(son, -1, sizeof son);
  dfs1(0, -1, 1);
  dfs2(0, 0);
}
int lca(int u, int v) {
  while (top[u] != top[v]) {
    if (dep[top[u]] < dep[top[v]]) swap(u, v);
    u = pa[top[u]];
  }
  return dep[u] < dep[v] ? u : v;
}
}  // namespace HLD
int mark[N], rmark[N], rmark2nod[N];
long long solve_ans = 0, now = 0;
set<int> st;
void ins_node(int u) {
  u = mark[u];
  if (!u) return;
  u = rmark2nod[u + 2];
  u = HLD::dfn[u];
  if (st.empty()) {
    st.insert(u);
    u = HLD::rdfn[u];
    now += HLD::val[u];
  } else {
    auto after = st.lower_bound(u);
    auto before = after;
    --before;
    if (after == st.end()) {
      int L = *before;
      L = HLD::rdfn[L];
      u = HLD::rdfn[u];
      int lca = HLD::lca(L, u);
      now -= HLD::val[lca];
      now += HLD::val[u];
      u = HLD::dfn[u];
      st.insert(u);
    } else if (after == st.begin()) {
      int R = *after;
      R = HLD::rdfn[R];
      u = HLD::rdfn[u];
      int lca = HLD::lca(R, u);
      now -= HLD::val[lca];
      now += HLD::val[u];
      u = HLD::dfn[u];
      st.insert(u);
    } else {
      int L = *before;
      int R = *after;
      L = HLD::rdfn[L];
      R = HLD::rdfn[R];
      now += HLD::val[HLD::lca(L, R)];
      u = HLD::rdfn[u];
      now -= HLD::val[HLD::lca(L, u)];
      now -= HLD::val[HLD::lca(R, u)];
      now += HLD::val[u];
      u = HLD::dfn[u];
      st.insert(u);
    }
  }
}
void ins_tree(int u) {
  ins_node(u);
  for (int i = g.head[u]; ~i; i = g.nxt[i]) ins_tree(g.to[i]);
}
int sz[N], son[N];
void init_sack(int u) {
  sz[u] = 1, son[u] = -1;
  for (int i = g.head[u]; ~i; i = g.nxt[i]) {
    int v = g.to[i];
    init_sack(v);
    sz[u] += sz[v];
    if (son[u] == -1 || sz[v] > sz[son[u]]) son[u] = v;
  }
}
void sack(int u, bool clr) {
  for (int i = g.head[u]; ~i; i = g.nxt[i])
    if (g.to[i] != son[u]) sack(g.to[i], true);
  if (son[u] != -1) sack(son[u], false);
  for (int i = g.head[u]; ~i; i = g.nxt[i])
    if (g.to[i] != son[u]) ins_tree(g.to[i]);
  ins_node(u);
  if (u) solve_ans += 1LL * now * (sam.len[u] - sam.len[sam.pa[u]]);
  if (clr) st.clear(), now = 0;
}
long long solve() {
  sam.init();
  int last = 0;
  for (int i = 1; i <= n - 2; ++i) last = sam.append(last, str[i] - 'a');
  g.init();
  for (int i = 1; i < sam.idx; ++i) g.link(sam.pa[i], i);
  last = 0;
  for (int i = 1; i <= n - 2; ++i) {
    last = sam.ch[last][str[i] - 'a'];
    mark[last] = i;
  }
  rsam.init();
  last = 0;
  for (int i = n; i >= 3; --i) last = rsam.append(last, str[i] - 'a');
  rg.init();
  for (int i = 1; i < rsam.idx; ++i) rg.link(rsam.pa[i], i);
  last = 0;
  for (int i = n; i >= 3; --i) {
    last = rsam.ch[last][str[i] - 'a'];
    rmark[last] = i;
    rmark2nod[i] = last;
  }
  HLD::init();
  init_sack(0);
  sack(0, false);
  return solve_ans;
}
int main() {
  _w = scanf("%s", str + 1);
  n = (int)strlen(str + 1);
  long long ans = 0;
  ans += solve_origin();
  if (n >= 2) {
    ans += solve_before();
    ans += solve_after();
  }
  if (n >= 3) {
    ans += solve();
  }
  printf("%lld\n", ans + 2);
  return 0;
}

```