Problem: Mahmoud and Ehab solved Dr. Evil's questions so he gave them the password of the door of the evil land. When they tried to open the door using it, the door gave them a final question to solve before they leave (yes, the door is digital, Dr. Evil is modern). If they don't solve it, all the work will be useless and they won't leave the evil land forever. Will you help them?

Mahmoud and Ehab are given n strings s1, s2, ... , sn numbered from 1 to n and q queries, Each query has one of the following forms:

  * 1 a b (1 ≤ a ≤ b ≤ n), For all the intervals [l;r] where (a ≤ l ≤ r ≤ b) find the maximum value of this expression:

(r - l + 1) * LCP(sl, sl + 1, ... , sr - 1, sr) where LCP(str1, str2, str3, ... ) is the length of the longest common prefix of the strings str1, str2, str3, ... .

  * 2 x y (1 ≤ x ≤ n) where y is a string, consisting of lowercase English letters. Change the string at position x to y.

Input

The first line of input contains 2 integers n and q (1 ≤ n ≤ 105, 1 ≤ q ≤ 105) – The number of strings and the number of queries, respectively.

The second line contains n strings stri consisting of lowercase English letters.

The next q lines describe the queries and may have one of the 2 forms:

  * 1 a b (1 ≤ a ≤ b ≤ n).
  * 2 x y (1 ≤ x ≤ n), where y is a string consisting of lowercase English letters.



the total length of all strings in input won't exceed 105

Output

For each query of first type output its answer in a new line.

Example

Input

5 9
mahmoud mahmoudbadawy drmahmoud drevil mahmoud
1 1 5
1 1 2
1 2 3
2 3 mahmoud
2 4 mahmoud
2 2 mahmouu
1 1 5
1 2 3
1 1 1


Output

14
14
13
30
12
7

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
long long gcd(long long a, long long b) { return b == 0 ? a : gcd(b, a % b); }
const int MAXLEN = 100000;
const int MAXN = 100000;
const int MAXQ = 100000;
const int MAXTN = MAXLEN + 1;
const int MAXLG = 16;
const int MAXSN = 4 * (MAXN - 1);
const int MAXZN = 4 * MAXN;
typedef struct TN {
  int d;
  int nxt[26];
  int par[MAXLG + 1];
} TN;
typedef struct SN {
  int best;
  vector<int> preidx, sufidx;
} SN;
int n, nq;
char s[MAXLEN + 1];
TN tn[MAXTN];
int ntn, troot;
int tpos[MAXN];
int qkind[MAXQ], ql[MAXQ], qr[MAXQ], qidx[MAXQ], qlen[MAXQ], qtpos[MAXQ];
int gettn(int par) {
  int ret = ntn++;
  tn[ret].d = par == -1 ? 0 : tn[par].d + 1;
  for (int i = (0); i < (26); ++i) tn[ret].nxt[i] = -1;
  tn[ret].par[0] = par == -1 ? ret : par;
  for (int i = (1); i <= (MAXLG); ++i)
    tn[ret].par[i] = tn[tn[ret].par[i - 1]].par[i - 1];
  return ret;
}
int tinsert() {
  int at = troot;
  for (int i = 0; s[i] != '\0'; ++i) {
    int x = s[i] - 'a';
    if (tn[at].nxt[x] == -1) tn[at].nxt[x] = gettn(at);
    at = tn[at].nxt[x];
  }
  return at;
}
int getlca(int a, int b) {
  if (tn[a].d < tn[b].d) swap(a, b);
  for (int k = MAXLG; k >= 0; --k)
    if (tn[a].d - (1 << k) >= tn[b].d) a = tn[a].par[k];
  for (int k = MAXLG; k >= 0; --k)
    if (tn[a].par[k] != tn[b].par[k]) a = tn[a].par[k], b = tn[b].par[k];
  return a == b ? a : tn[a].par[0];
}
int lcp[MAXN - 1];
SN sn[MAXSN];
void print(const SN &a) {
  printf("[");
  for (int i = (0); i < (((int)(a.preidx).size())); ++i) {
    if (i != 0) printf(",");
    printf("%d", a.preidx[i]);
  }
  printf("][");
  for (int i = (0); i < (((int)(a.sufidx).size())); ++i) {
    if (i != 0) printf(",");
    printf("%d", a.sufidx[i]);
  }
  printf("]->%d", a.best);
}
int calc(int l, int r, int mn) { return (r - l + 2) * mn; }
SN makesn(int idx) {
  SN ret;
  ret.best = calc(idx, idx, lcp[idx]);
  ret.preidx.push_back(idx);
  ret.sufidx.push_back(idx);
  return ret;
}
SN combine(const SN &a, const SN &b) {
  SN ret;
  ret.best = max(a.best, b.best);
  int ai = ((int)(a.sufidx).size()) - 1, bi = ((int)(b.preidx).size()) - 1;
  while (true) {
    if (lcp[a.sufidx[ai]] >= lcp[b.preidx[bi]]) {
      if (ai == 0) {
        for (int i = (0); i <= (bi); ++i) ret.preidx.push_back(b.preidx[i]);
        for (int i = (0); i < (((int)(a.preidx).size())); ++i)
          if (lcp[a.preidx[i]] == lcp[ret.preidx.back()])
            ret.preidx[((int)(ret.preidx).size()) - 1] = a.preidx[i];
          else
            ret.preidx.push_back(a.preidx[i]);
        ret.sufidx = b.sufidx;
        break;
      } else {
        int cur =
            calc(a.sufidx[ai - 1] + 1, b.preidx[bi] - 1, lcp[a.sufidx[ai]]);
        if (cur > ret.best) ret.best = cur;
        --ai;
      }
    } else {
      if (bi == 0) {
        ret.preidx = a.preidx;
        for (int i = (0); i <= (ai); ++i) ret.sufidx.push_back(a.sufidx[i]);
        for (int i = (0); i < (((int)(b.sufidx).size())); ++i)
          if (lcp[b.sufidx[i]] == lcp[ret.sufidx.back()])
            ret.sufidx[((int)(ret.sufidx).size()) - 1] = b.sufidx[i];
          else
            ret.sufidx.push_back(b.sufidx[i]);
        break;
      } else {
        int cur =
            calc(a.sufidx[ai] + 1, b.preidx[bi - 1] - 1, lcp[b.preidx[bi]]);
        if (cur > ret.best) ret.best = cur;
        --bi;
      }
    }
  }
  int l = ret.preidx.back(), r = ret.sufidx.back();
  ret.best = max(ret.best, calc(l, r, lcp[ret.preidx[0]]));
  for (int i = (1); i < (((int)(ret.preidx).size())); ++i)
    ret.best =
        max(ret.best, calc(l, ret.preidx[i - 1] - 1, lcp[ret.preidx[i]]));
  for (int i = (1); i < (((int)(ret.sufidx).size())); ++i)
    ret.best =
        max(ret.best, calc(ret.sufidx[i - 1] + 1, r, lcp[ret.sufidx[i]]));
  return ret;
}
void sinit(int x, int l, int r) {
  if (l == r) {
    sn[x] = makesn(l);
  } else {
    int m = l + (r - l) / 2;
    sinit(2 * x + 1, l, m);
    sinit(2 * x + 2, m + 1, r);
    sn[x] = combine(sn[2 * x + 1], sn[2 * x + 2]);
  }
}
void sset(int x, int l, int r, int IDX) {
  if (l == r) {
    sn[x] = makesn(l);
  } else {
    int m = l + (r - l) / 2;
    if (IDX <= m)
      sset(2 * x + 1, l, m, IDX);
    else
      sset(2 * x + 2, m + 1, r, IDX);
    sn[x] = combine(sn[2 * x + 1], sn[2 * x + 2]);
  }
}
SN sget(int x, int l, int r, int L, int R) {
  if (L <= l && r <= R) return sn[x];
  int m = l + (r - l) / 2;
  if (R <= m) return sget(2 * x + 1, l, m, L, R);
  if (m + 1 <= L) return sget(2 * x + 2, m + 1, r, L, R);
  return combine(sget(2 * x + 1, l, m, L, R), sget(2 * x + 2, m + 1, r, L, R));
}
int len[MAXN];
int zn[MAXZN];
void zinit(int x, int l, int r) {
  if (l == r) {
    zn[x] = len[l];
  } else {
    int m = l + (r - l) / 2;
    zinit(2 * x + 1, l, m);
    zinit(2 * x + 2, m + 1, r);
    zn[x] = max(zn[2 * x + 1], zn[2 * x + 2]);
  }
}
void zset(int x, int l, int r, int IDX) {
  if (l == r) {
    zn[x] = len[l];
  } else {
    int m = l + (r - l) / 2;
    if (IDX <= m)
      zset(2 * x + 1, l, m, IDX);
    else
      zset(2 * x + 2, m + 1, r, IDX);
    zn[x] = max(zn[2 * x + 1], zn[2 * x + 2]);
  }
}
int zget(int x, int l, int r, int L, int R) {
  if (L <= l && r <= R) return zn[x];
  int m = l + (r - l) / 2;
  if (R <= m) return zget(2 * x + 1, l, m, L, R);
  if (m + 1 <= L) return zget(2 * x + 2, m + 1, r, L, R);
  return max(zget(2 * x + 1, l, m, L, R), zget(2 * x + 2, m + 1, r, L, R));
}
int ans[MAXQ];
void solve() {
  for (int i = (0); i < (n - 1); ++i)
    lcp[i] = tn[getlca(tpos[i], tpos[i + 1])].d;
  if (n >= 2) sinit(0, 0, n - 2);
  zinit(0, 0, n - 1);
  for (int i = (0); i < (nq); ++i) {
    if (qkind[i] == 1) {
      ans[i] = zget(0, 0, n - 1, ql[i], qr[i]);
      if (ql[i] != qr[i]) {
        SN cur = sget(0, 0, n - 2, ql[i], qr[i] - 1);
        if (cur.best > ans[i]) ans[i] = cur.best;
      }
    }
    if (qkind[i] == 2) {
      int idx = qidx[i];
      tpos[idx] = qtpos[i];
      len[idx] = qlen[i];
      zset(0, 0, n - 1, idx);
      if (idx >= 1) {
        lcp[idx - 1] = tn[getlca(tpos[idx - 1], tpos[idx])].d;
        sset(0, 0, n - 2, idx - 1);
      }
      if (idx + 1 < n) {
        lcp[idx] = tn[getlca(tpos[idx], tpos[idx + 1])].d;
        sset(0, 0, n - 2, idx);
      }
    }
  }
}
void run() {
  ntn = 0;
  troot = gettn(-1);
  scanf("%d%d", &n, &nq);
  for (int i = (0); i < (n); ++i) {
    scanf("%s", s);
    len[i] = strlen(s), tpos[i] = tinsert();
  }
  for (int i = (0); i < (nq); ++i) {
    scanf("%d", &qkind[i]);
    if (qkind[i] == 1) {
      scanf("%d%d", &ql[i], &qr[i]);
      --ql[i], --qr[i];
    }
    if (qkind[i] == 2) {
      scanf("%d%s", &qidx[i], s);
      --qidx[i], qlen[i] = strlen(s), qtpos[i] = tinsert();
    }
  }
  solve();
  for (int i = (0); i < (nq); ++i)
    if (qkind[i] == 1) printf("%d\n", ans[i]);
}
string ss[MAXN];
string os[MAXN];
string qs[MAXQ];
int chk[MAXQ];
int bflcp(const string &a, const string &b) {
  int ret = 0;
  while (ret < ((int)(a).size()) && ret < ((int)(b).size()) && a[ret] == b[ret])
    ++ret;
  return ret;
}
int bf(int l, int r) {
  int ret = 0;
  vector<pair<int, int> > stck;
  for (int i = (l); i <= (r); ++i) {
    ret = max(ret, ((int)(ss[i]).size()));
    if (i != l) {
      int lcp = bflcp(ss[i - 1], ss[i]);
      while (((int)(stck).size()) > 0 && lcp <= stck.back().first) {
        int cur = calc(((int)(stck).size()) == 1
                           ? l
                           : stck[((int)(stck).size()) - 2].second + 1,
                       i - 2, stck.back().first);
        if (cur > ret) ret = cur;
        stck.pop_back();
      }
      stck.push_back(make_pair(lcp, i - 1));
    }
  }
  while (((int)(stck).size()) > 0) {
    int cur = calc(((int)(stck).size()) == 1
                       ? l
                       : stck[((int)(stck).size()) - 2].second + 1,
                   r - 1, stck.back().first);
    if (cur > ret) ret = cur;
    stck.pop_back();
  }
  return ret;
}
void stress() {
  for (int rep = (0); rep < (10000); ++rep) {
    ntn = 0;
    troot = gettn(-1);
    n = 100;
    nq = 100;
    int slen = 5;
    for (int i = (0); i < (n); ++i) {
      for (int j = (0); j < (slen); ++j) s[j] = 'a' + rand() % 2;
      s[slen] = '\0';
      os[i] = ss[i] = string(s);
      len[i] = strlen(s), tpos[i] = tinsert();
    }
    for (int i = (0); i < (nq); ++i) {
      qkind[i] = 1 + rand() % 2;
      if (qkind[i] == 1) {
        ql[i] = rand() % n, qr[i] = rand() % n;
        if (ql[i] > qr[i]) swap(ql[i], qr[i]);
        chk[i] = bf(ql[i], qr[i]);
      }
      if (qkind[i] == 2) {
        qidx[i] = rand() % n;
        for (int j = (0); j < (slen); ++j) s[j] = 'a' + rand() % 2;
        s[slen] = '\0';
        qs[i] = ss[qidx[i]] = string(s);
        qlen[i] = strlen(s), qtpos[i] = tinsert();
      }
    }
    solve();
    bool ok = true;
    for (int i = (0); i < (nq); ++i)
      if (qkind[i] == 1 && chk[i] != ans[i]) {
        printf("it%d: err in q%d: expected %d but got %d\n", rep, i, chk[i],
               ans[i]);
        printf("%d %d\n", n, nq);
        for (int j = (0); j < (n); ++j) {
          if (j != 0) printf(" ");
          printf("%s", os[j].c_str());
        }
        puts("");
        for (int j = (0); j < (nq); ++j) {
          if (qkind[j] == 1) printf("1 %d %d\n", ql[j] + 1, qr[j] + 1);
          if (qkind[j] == 2) printf("2 %d %s\n", qidx[j] + 1, qs[j].c_str());
        }
        ok = false;
        break;
      }
    if (ok) printf(".");
  }
}
void stresstime() {
  ntn = 0;
  troot = gettn(-1);
  n = MAXN;
  nq = MAXQ;
  int slen = 1;
  for (int i = (0); i < (n); ++i) {
    for (int j = (0); j < (slen); ++j) s[j] = 'a' + rand() % 2;
    s[slen] = '\0';
    len[i] = strlen(s), tpos[i] = tinsert();
  }
  for (int i = (0); i < (nq); ++i) {
    qkind[i] = 1;
    if (qkind[i] == 1) {
      ql[i] = rand() % n, qr[i] = rand() % n;
      if (ql[i] > qr[i]) swap(ql[i], qr[i]);
      chk[i] = bf(ql[i], qr[i]);
    }
    if (qkind[i] == 2) {
      qidx[i] = rand() % n;
      for (int j = (0); j < (slen); ++j) s[j] = 'a' + rand() % 2;
      s[slen] = '\0';
      qs[i] = ss[qidx[i]] = string(s);
      qlen[i] = strlen(s), qtpos[i] = tinsert();
    }
  }
  solve();
}
int main() {
  run();
  return 0;
}