#include <bits/stdc++.h>
using namespace std;
const int MOD = (int)1e9 + 7;
const int FFTMOD = 119 << 23 | 1;
const int INF = (int)1e9 + 23111992;
const long long LINF = (long long)1e18 + 23111992;
const long double PI = acos((long double)-1);
const long double EPS = 1e-9;
inline long long gcd(long long a, long long b) {
  long long r;
  while (b) {
    r = a % b;
    a = b;
    b = r;
  }
  return a;
}
inline long long lcm(long long a, long long b) { return a / gcd(a, b) * b; }
inline long long fpow(long long n, long long k, int p = MOD) {
  long long r = 1;
  for (; k; k >>= 1) {
    if (k & 1) r = r * n % p;
    n = n * n % p;
  }
  return r;
}
template <class T>
inline int chkmin(T& a, const T& val) {
  return val < a ? a = val, 1 : 0;
}
template <class T>
inline int chkmax(T& a, const T& val) {
  return a < val ? a = val, 1 : 0;
}
inline unsigned long long isqrt(unsigned long long k) {
  unsigned long long r = sqrt(k) + 1;
  while (r * r > k) r--;
  return r;
}
inline long long icbrt(long long k) {
  long long r = cbrt(k) + 1;
  while (r * r * r > k) r--;
  return r;
}
inline void addmod(int& a, int val, int p = MOD) {
  if ((a = (a + val)) >= p) a -= p;
}
inline void submod(int& a, int val, int p = MOD) {
  if ((a = (a - val)) < 0) a += p;
}
inline int mult(int a, int b, int p = MOD) { return (long long)a * b % p; }
inline int inv(int a, int p = MOD) { return fpow(a, p - 2, p); }
inline int sign(long double x) { return x < -EPS ? -1 : x > +EPS; }
inline int sign(long double x, long double y) { return sign(x - y); }
mt19937 mt(chrono::high_resolution_clock::now().time_since_epoch().count());
inline int myrand() { return abs((int)mt()); }
struct node_t {
  int ans;
  int mn, mx;
  int mx_pref, mx_suff;
  node_t() {
    ans = 0;
    mn = +INF;
    mx = mx_pref = mx_suff = -INF;
  }
};
node_t merge(node_t a, node_t b) {
  node_t c;
  c.ans = max(a.ans, b.ans);
  chkmax(c.ans, a.mx_pref + b.mx);
  chkmax(c.ans, a.mx + b.mx_suff);
  c.mn = min(a.mn, b.mn);
  c.mx = max(a.mx, b.mx);
  c.mx_pref = max(a.mx_pref, b.mx_pref);
  c.mx_suff = max(a.mx_suff, b.mx_suff);
  chkmax(c.mx_pref, a.mx - b.mn - b.mn);
  chkmax(c.mx_suff, b.mx - a.mn - a.mn);
  return c;
}
const int maxn = 3e5 + 5;
int n, q;
node_t st[maxn << 2];
int lz[maxn << 2];
void push(int p, int L, int R) {
  if (lz[p]) {
    st[p].mn += lz[p], st[p].mx += lz[p], st[p].mx_pref -= lz[p],
        st[p].mx_suff -= lz[p];
    if (L < R) {
      for (int i = (p << 1); i < (p + 1 << 1); ++i) {
        lz[i] += lz[p];
      }
    }
    lz[p] = 0;
  }
}
void upd(int p, int l, int r, int L, int R, int val) {
  push(p, L, R);
  if (r < L || R < l) return;
  if (l <= L && R <= r) {
    lz[p] = val;
    push(p, L, R);
    return;
  }
  upd(p << 1, l, r, L, L + R >> 1, val);
  upd(p << 1 | 1, l, r, (L + R >> 1) + 1, R, val);
  st[p] = merge(st[p << 1], st[p << 1 | 1]);
}
void build(int p, int L, int R, vector<int>& a) {
  if (L == R) {
    st[p].mn = st[p].mx = a[L];
    st[p].mx_pref = st[p].mx_suff = -a[L];
    return;
  }
  build(p << 1, L, L + R >> 1, a);
  build(p << 1 | 1, (L + R >> 1) + 1, R, a);
  st[p] = merge(st[p << 1], st[p << 1 | 1]);
}
void chemthan() {
  cin >> n >> q, n = 2 * n - 2;
  string s;
  cin >> s;
  vector<int> a(n);
  int sum = 0;
  for (int i = (0); i < (n); ++i) {
    sum += s[i] == '(' ? 1 : -1;
    a[i] = sum;
  }
  build(1, 0, n - 1, a);
  cout << st[1].ans << "\n";
  while (q--) {
    int u, v;
    cin >> u >> v;
    u--, v--;
    for (int e : {u, v}) {
      upd(1, e, n - 1, 0, n - 1, s[e] == '(' ? -1 : 1);
    }
    swap(s[u], s[v]);
    for (int e : {u, v}) {
      upd(1, e, n - 1, 0, n - 1, s[e] == '(' ? 1 : -1);
    }
    cout << st[1].ans << "\n";
  }
}
int main(int argc, char* argv[]) {
  ios_base::sync_with_stdio(0), cin.tie(0);
  if (argc > 1) {
    assert(freopen(argv[1], "r", stdin));
  }
  if (argc > 2) {
    assert(freopen(argv[2], "wb", stdout));
  }
  chemthan();
  cerr << "\nTime elapsed: " << 1000 * clock() / CLOCKS_PER_SEC << "ms\n";
  return 0;
}
