#include <bits/stdc++.h>
using namespace std;
const int N = 234567;
const int LOG = 18;
const int ALPHA = 26;
const int base = 2333;
const int md0 = 1e9 + 7;
const int md1 = 1e9 + 9;
struct hash_t {
  int hash0, hash1;
  hash_t(int hash0 = 0, int hash1 = 0) : hash0(hash0), hash1(hash1) {}
  hash_t operator+(const int &x) const {
    return hash_t((hash0 + x) % md0, (hash1 + x) % md1);
  };
  hash_t operator*(const int &x) const {
    return hash_t((long long)hash0 * x % md0, (long long)hash1 * x % md1);
  }
  hash_t operator+(const hash_t &x) const {
    return hash_t((hash0 + x.hash0) % md0, (hash1 + x.hash1) % md1);
  };
  hash_t operator-(const hash_t &x) const {
    return hash_t((hash0 + md0 - x.hash0) % md0, (hash1 + md1 - x.hash1) % md1);
  };
  hash_t operator*(const hash_t &x) const {
    return hash_t((long long)hash0 * x.hash0 % md0,
                  (long long)hash1 * x.hash1 % md1);
  }
  long long get() { return (long long)hash0 * md1 + hash1; }
} ha[N], hb[N], power[N];
struct palindrome_tree_t {
  int n, total, p[N], pos[N], value[N], parent[N], go[N][ALPHA],
      ancestor[LOG][N];
  char s[N];
  palindrome_tree_t() {
    parent[0] = 1;
    value[1] = -1;
    total = 1;
    p[0] = 1;
  }
  int extend(int p, int w, int n) {
    while (s[n] != s[n - value[p] - 1]) {
      p = parent[p];
    }
    if (!go[p][w]) {
      int q = ++total, k = parent[p];
      while (s[n] != s[n - value[k] - 1]) {
        k = parent[k];
      }
      value[q] = value[p] + 2;
      parent[q] = go[k][w];
      go[p][w] = q;
      pos[q] = n;
    }
    return go[p][w];
  }
  void init() {
    for (int i = 1; i <= n; ++i) {
      p[i] = extend(p[i - 1], s[i] - 'a', i);
    }
    for (int i = 0; i <= total; ++i) {
      ancestor[0][i] = parent[i];
    }
    for (int i = 1; i < LOG; ++i) {
      for (int j = 0; j <= total; ++j) {
        ancestor[i][j] = ancestor[i - 1][ancestor[i - 1][j]];
      }
    }
  }
  int query(int r, int length) {
    r = p[r];
    if (value[r] <= length) {
      return value[r];
    }
    for (int i = LOG - 1; ~i; --i) {
      if (value[ancestor[i][r]] > length) {
        r = ancestor[i][r];
      }
    }
    return value[parent[r]];
  }
  bool check(int r, int length) {
    r = p[r];
    for (int i = LOG - 1; ~i; --i) {
      if (value[ancestor[i][r]] >= length) {
        r = ancestor[i][r];
      }
    }
    return value[r] == length;
  }
} A, B, RA, RB;
map<long long, int> fa, fb, ga, gb;
long long answer;
char a[N], b[N];
int n, m;
hash_t get_hash(hash_t *h, int l, int r) {
  return h[r] - h[l - 1] * power[r - l + 1];
}
int main() {
  scanf("%s %s", a + 1, b + 1);
  n = strlen(a + 1);
  m = strlen(b + 1);
  A.n = RA.n = n;
  B.n = RB.n = m;
  for (int i = 1; i <= n; ++i) {
    A.s[i] = RA.s[n - i + 1] = a[i];
    ha[i] = ha[i - 1] * base + a[i];
  }
  for (int i = 1; i <= m; ++i) {
    B.s[i] = RB.s[m - i + 1] = b[i];
    hb[i] = hb[i - 1] * base + b[i];
  }
  power[0] = hash_t(1, 1);
  for (int i = 1; i <= max(n, m); ++i) {
    power[i] = power[i - 1] * base;
  }
  A.init();
  B.init();
  RA.init();
  RB.init();
  answer = (long long)(A.total - 1) * (B.total - 1);
  for (int i = 2; i <= A.total; ++i) {
    ++fa[get_hash(ha, A.pos[i] - A.value[i] + 1, A.pos[i]).get()];
    int p = A.parent[i];
    if (p < 2) {
      continue;
    }
    int l = A.pos[i] - (A.value[i] - A.value[p]) + 1, r = A.pos[i];
    if (A.value[i] <= A.value[p] << 1) {
      ++ga[get_hash(ha, l, r).get()];
    }
  }
  for (int i = 2; i <= B.total; ++i) {
    ++fb[get_hash(hb, B.pos[i] - B.value[i] + 1, B.pos[i]).get()];
    int p = B.parent[i];
    if (p < 2) {
      continue;
    }
    int l = B.pos[i] - B.value[i] + 1, r = B.pos[i] - B.value[p];
    if (B.value[i] <= B.value[p] << 1) {
      ++gb[get_hash(hb, l, r).get()];
    }
  }
  for (int i = 2; i <= A.total; ++i) {
    int p = A.parent[i];
    if (p < 2) {
      continue;
    }
    int l = A.pos[i] - (A.value[i] - A.value[p]) + 1, r = A.pos[i];
    long long value = get_hash(ha, l, r).get();
    if (gb.count(value)) {
      answer -= gb[value];
    }
    int longest_palindrome_suffix = A.query(r, r - l + 1);
    if (longest_palindrome_suffix == r - l + 1) {
      continue;
    }
    if (RA.check(n - l + 1, r - l + 1 - longest_palindrome_suffix)) {
      int length = r - l + 1 - longest_palindrome_suffix;
      if (fb.count(get_hash(ha, l, l + length - 1).get()) &&
          fb.count((get_hash(ha, l, r) * power[length] +
                    get_hash(ha, l, l + length - 1))
                       .get())) {
        --answer;
      }
      continue;
    }
    int longest_palindrome_prefix = RA.query(n - l + 1, r - l + 1);
    if (A.check(r, r - l + 1 - longest_palindrome_prefix)) {
      int length = longest_palindrome_prefix;
      if (fb.count(get_hash(ha, l, l + length - 1).get()) &&
          fb.count((get_hash(ha, l, r) * power[length] +
                    get_hash(ha, l, l + length - 1))
                       .get())) {
        --answer;
      }
      continue;
    }
  }
  for (int i = 2; i <= B.total; ++i) {
    int p = B.parent[i];
    if (p < 2) {
      continue;
    }
    int l = B.pos[i] - B.value[i] + 1, r = B.pos[i] - B.value[p];
    long long value = get_hash(hb, l, r).get();
    if (ga.count(value)) {
      answer -= ga[value];
    }
    int longest_palindrome_suffix = B.query(r, r - l + 1);
    if (longest_palindrome_suffix == r - l + 1) {
      continue;
    }
    if (RB.check(m - l + 1, r - l + 1 - longest_palindrome_suffix)) {
      int length = longest_palindrome_suffix;
      if (fa.count(get_hash(hb, r - length + 1, r).get()) &&
          fa.count((get_hash(hb, r - length + 1, r) * power[r - l + 1] +
                    get_hash(hb, l, r))
                       .get())) {
        --answer;
      }
      continue;
    }
    int longest_palindrome_prefix = RB.query(m - l + 1, r - l + 1);
    if (B.check(r, r - l + 1 - longest_palindrome_prefix)) {
      int length = r - l + 1 - longest_palindrome_prefix;
      if (fa.count(get_hash(hb, r - length + 1, r).get()) &&
          fa.count((get_hash(hb, r - length + 1, r) * power[r - l + 1] +
                    get_hash(hb, l, r))
                       .get())) {
        --answer;
      }
      continue;
    }
  }
  for (int i = 2; i <= A.total; ++i) {
    int p = A.parent[i];
    if (p < 2) {
      continue;
    }
    int l = A.pos[i] - (A.value[i] - A.value[p]) + 1, r = A.pos[i];
    if (A.value[i] > A.value[p] << 1) {
      ++ga[get_hash(ha, l, r).get()];
    }
  }
  for (int i = 2; i <= B.total; ++i) {
    int p = B.parent[i];
    if (p < 2) {
      continue;
    }
    int l = B.pos[i] - B.value[i] + 1, r = B.pos[i] - B.value[p];
    if (B.value[i] > B.value[p] << 1) {
      ++gb[get_hash(hb, l, r).get()];
    }
  }
  for (auto p : ga) {
    answer += (long long)p.second * gb[p.first];
  }
  printf("%lld\n", answer);
  return 0;
}

### Prompt

Your challenge is to write a CPP solution to the following problem:

After learning some fancy algorithms about palindromes, Chouti found palindromes very interesting, so he wants to challenge you with this problem.

Chouti has got two strings A and B. Since he likes [palindromes](https://en.wikipedia.org/wiki/Palindrome), he would like to pick a as some non-empty palindromic substring of A and b as some non-empty palindromic substring of B. Concatenating them, he will get string ab.

Chouti thinks strings he could get this way are interesting, so he wants to know how many different strings he can get.

Input

The first line contains a single string A (1 ≤ |A| ≤ 2 ⋅ 10^5).

The second line contains a single string B (1 ≤ |B| ≤ 2 ⋅ 10^5).

Strings A and B contain only lowercase English letters.

Output

The first and only line should contain a single integer — the number of possible strings.

Examples

Input

aa
aba


Output

6


Input

aaba
abaa


Output

15

Note

In the first example, attainable strings are 

  * "a" + "a" = "aa", 
  * "aa" + "a" = "aaa", 
  * "aa" + "aba" = "aaaba", 
  * "aa" + "b" = "aab", 
  * "a" + "aba" = "aaba", 
  * "a" + "b" = "ab". 



In the second example, attainable strings are "aa", "aaa", "aaaa", "aaaba", "aab", "aaba", "ab", "abaa", "abaaa", "abaaba", "abab", "ba", "baa", "baba", "bb".

Notice that though "a"+"aa"="aa"+"a"="aaa", "aaa" will only be counted once.

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
const int N = 234567;
const int LOG = 18;
const int ALPHA = 26;
const int base = 2333;
const int md0 = 1e9 + 7;
const int md1 = 1e9 + 9;
struct hash_t {
  int hash0, hash1;
  hash_t(int hash0 = 0, int hash1 = 0) : hash0(hash0), hash1(hash1) {}
  hash_t operator+(const int &x) const {
    return hash_t((hash0 + x) % md0, (hash1 + x) % md1);
  };
  hash_t operator*(const int &x) const {
    return hash_t((long long)hash0 * x % md0, (long long)hash1 * x % md1);
  }
  hash_t operator+(const hash_t &x) const {
    return hash_t((hash0 + x.hash0) % md0, (hash1 + x.hash1) % md1);
  };
  hash_t operator-(const hash_t &x) const {
    return hash_t((hash0 + md0 - x.hash0) % md0, (hash1 + md1 - x.hash1) % md1);
  };
  hash_t operator*(const hash_t &x) const {
    return hash_t((long long)hash0 * x.hash0 % md0,
                  (long long)hash1 * x.hash1 % md1);
  }
  long long get() { return (long long)hash0 * md1 + hash1; }
} ha[N], hb[N], power[N];
struct palindrome_tree_t {
  int n, total, p[N], pos[N], value[N], parent[N], go[N][ALPHA],
      ancestor[LOG][N];
  char s[N];
  palindrome_tree_t() {
    parent[0] = 1;
    value[1] = -1;
    total = 1;
    p[0] = 1;
  }
  int extend(int p, int w, int n) {
    while (s[n] != s[n - value[p] - 1]) {
      p = parent[p];
    }
    if (!go[p][w]) {
      int q = ++total, k = parent[p];
      while (s[n] != s[n - value[k] - 1]) {
        k = parent[k];
      }
      value[q] = value[p] + 2;
      parent[q] = go[k][w];
      go[p][w] = q;
      pos[q] = n;
    }
    return go[p][w];
  }
  void init() {
    for (int i = 1; i <= n; ++i) {
      p[i] = extend(p[i - 1], s[i] - 'a', i);
    }
    for (int i = 0; i <= total; ++i) {
      ancestor[0][i] = parent[i];
    }
    for (int i = 1; i < LOG; ++i) {
      for (int j = 0; j <= total; ++j) {
        ancestor[i][j] = ancestor[i - 1][ancestor[i - 1][j]];
      }
    }
  }
  int query(int r, int length) {
    r = p[r];
    if (value[r] <= length) {
      return value[r];
    }
    for (int i = LOG - 1; ~i; --i) {
      if (value[ancestor[i][r]] > length) {
        r = ancestor[i][r];
      }
    }
    return value[parent[r]];
  }
  bool check(int r, int length) {
    r = p[r];
    for (int i = LOG - 1; ~i; --i) {
      if (value[ancestor[i][r]] >= length) {
        r = ancestor[i][r];
      }
    }
    return value[r] == length;
  }
} A, B, RA, RB;
map<long long, int> fa, fb, ga, gb;
long long answer;
char a[N], b[N];
int n, m;
hash_t get_hash(hash_t *h, int l, int r) {
  return h[r] - h[l - 1] * power[r - l + 1];
}
int main() {
  scanf("%s %s", a + 1, b + 1);
  n = strlen(a + 1);
  m = strlen(b + 1);
  A.n = RA.n = n;
  B.n = RB.n = m;
  for (int i = 1; i <= n; ++i) {
    A.s[i] = RA.s[n - i + 1] = a[i];
    ha[i] = ha[i - 1] * base + a[i];
  }
  for (int i = 1; i <= m; ++i) {
    B.s[i] = RB.s[m - i + 1] = b[i];
    hb[i] = hb[i - 1] * base + b[i];
  }
  power[0] = hash_t(1, 1);
  for (int i = 1; i <= max(n, m); ++i) {
    power[i] = power[i - 1] * base;
  }
  A.init();
  B.init();
  RA.init();
  RB.init();
  answer = (long long)(A.total - 1) * (B.total - 1);
  for (int i = 2; i <= A.total; ++i) {
    ++fa[get_hash(ha, A.pos[i] - A.value[i] + 1, A.pos[i]).get()];
    int p = A.parent[i];
    if (p < 2) {
      continue;
    }
    int l = A.pos[i] - (A.value[i] - A.value[p]) + 1, r = A.pos[i];
    if (A.value[i] <= A.value[p] << 1) {
      ++ga[get_hash(ha, l, r).get()];
    }
  }
  for (int i = 2; i <= B.total; ++i) {
    ++fb[get_hash(hb, B.pos[i] - B.value[i] + 1, B.pos[i]).get()];
    int p = B.parent[i];
    if (p < 2) {
      continue;
    }
    int l = B.pos[i] - B.value[i] + 1, r = B.pos[i] - B.value[p];
    if (B.value[i] <= B.value[p] << 1) {
      ++gb[get_hash(hb, l, r).get()];
    }
  }
  for (int i = 2; i <= A.total; ++i) {
    int p = A.parent[i];
    if (p < 2) {
      continue;
    }
    int l = A.pos[i] - (A.value[i] - A.value[p]) + 1, r = A.pos[i];
    long long value = get_hash(ha, l, r).get();
    if (gb.count(value)) {
      answer -= gb[value];
    }
    int longest_palindrome_suffix = A.query(r, r - l + 1);
    if (longest_palindrome_suffix == r - l + 1) {
      continue;
    }
    if (RA.check(n - l + 1, r - l + 1 - longest_palindrome_suffix)) {
      int length = r - l + 1 - longest_palindrome_suffix;
      if (fb.count(get_hash(ha, l, l + length - 1).get()) &&
          fb.count((get_hash(ha, l, r) * power[length] +
                    get_hash(ha, l, l + length - 1))
                       .get())) {
        --answer;
      }
      continue;
    }
    int longest_palindrome_prefix = RA.query(n - l + 1, r - l + 1);
    if (A.check(r, r - l + 1 - longest_palindrome_prefix)) {
      int length = longest_palindrome_prefix;
      if (fb.count(get_hash(ha, l, l + length - 1).get()) &&
          fb.count((get_hash(ha, l, r) * power[length] +
                    get_hash(ha, l, l + length - 1))
                       .get())) {
        --answer;
      }
      continue;
    }
  }
  for (int i = 2; i <= B.total; ++i) {
    int p = B.parent[i];
    if (p < 2) {
      continue;
    }
    int l = B.pos[i] - B.value[i] + 1, r = B.pos[i] - B.value[p];
    long long value = get_hash(hb, l, r).get();
    if (ga.count(value)) {
      answer -= ga[value];
    }
    int longest_palindrome_suffix = B.query(r, r - l + 1);
    if (longest_palindrome_suffix == r - l + 1) {
      continue;
    }
    if (RB.check(m - l + 1, r - l + 1 - longest_palindrome_suffix)) {
      int length = longest_palindrome_suffix;
      if (fa.count(get_hash(hb, r - length + 1, r).get()) &&
          fa.count((get_hash(hb, r - length + 1, r) * power[r - l + 1] +
                    get_hash(hb, l, r))
                       .get())) {
        --answer;
      }
      continue;
    }
    int longest_palindrome_prefix = RB.query(m - l + 1, r - l + 1);
    if (B.check(r, r - l + 1 - longest_palindrome_prefix)) {
      int length = r - l + 1 - longest_palindrome_prefix;
      if (fa.count(get_hash(hb, r - length + 1, r).get()) &&
          fa.count((get_hash(hb, r - length + 1, r) * power[r - l + 1] +
                    get_hash(hb, l, r))
                       .get())) {
        --answer;
      }
      continue;
    }
  }
  for (int i = 2; i <= A.total; ++i) {
    int p = A.parent[i];
    if (p < 2) {
      continue;
    }
    int l = A.pos[i] - (A.value[i] - A.value[p]) + 1, r = A.pos[i];
    if (A.value[i] > A.value[p] << 1) {
      ++ga[get_hash(ha, l, r).get()];
    }
  }
  for (int i = 2; i <= B.total; ++i) {
    int p = B.parent[i];
    if (p < 2) {
      continue;
    }
    int l = B.pos[i] - B.value[i] + 1, r = B.pos[i] - B.value[p];
    if (B.value[i] > B.value[p] << 1) {
      ++gb[get_hash(hb, l, r).get()];
    }
  }
  for (auto p : ga) {
    answer += (long long)p.second * gb[p.first];
  }
  printf("%lld\n", answer);
  return 0;
}

```