day 4, D 100

#include <bits/stdc++.h>
// tiom4eg's precompiler options
// POGGERS POGGERS POGGERS POGGERS POGGERS POGGERS POGGERS
// IO settings
#define fastIO ios_base::sync_with_stdio(false); cin.tie(0)
// Quick types
#define ll long long
#define ld long double
#define ull unsigned long long
#define pii pair <int, int>
#define vi vector <int>
#define mi vector <vector <int>>
// Quick functions
#define endl "\n"
#define F first
#define S second
#define all(a) a.begin(), a.end()
//#define sz(a) (int)(a.size())
#define pb push_back
#define mp make_pair
// Quick fors
#define FOR(i, a, b) for (int i = a; i < b; ++i)
#define FORS(i, a, b, c) for (int i = a; i < b; i += c)
#define RFOR(i, a, b) for (int i = a; i >= b; --i)
#define EACH(e, a) for (auto& e : a)
// Pragmas
#ifndef TIOM4EG
#pragma GCC optimize("O3") // let the chaos begin!
#pragma GCC target("avx,avx2,bmi,bmi2,popcnt,lzcnt,tune=native")
#pragma GCC comment(linker, "/stack:200000000")
#endif
// PBDS
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#define ordered_set tree <int, null_type, less <int>, rb_tree_tag, tree_order_statistics_node_update>
#define ook order_of_key
#define fbo find_by_order
using namespace __gnu_pbds;
// POGGERS POGGERS POGGERS POGGERS POGGERS POGGERS POGGERS
using namespace std;
mt19937 rng(chrono::duration_cast<chrono::milliseconds>(chrono::system_clock::now().time_since_epoch()).count());
#define int long long
const int INF = 1e9 + 7, MD = 998244353, MAX = 300005, R = 1 << 19, MOD = 1e9 + 7, MOD2 = 1e9 + 9, MOD12 = MOD * MOD, MOD22 = MOD2 * MOD2, LG = 20, B1 = 300007, B2 = 107, S = 10008;
const ll INFLL = 1e18 + 7;

struct Fenwick {
    vi t;
    int s;
    void init(int n) {
        s = n + 3;
        t.resize(s);
    }
    void upd(int p, int x) { for (; p < s; p += p & -p) t[p] += x; }
    int get(int p) {
        int r = 0;
        for (; p; p -= p & -p) r += t[p];
        return r;
    }
};

int p[MAX], w[MAX], sz[MAX], o[MAX], re[MAX];
Fenwick t, v[MAX];

signed main() {
    fastIO;
    int n, q, s = 1, c = 1; cin >> n >> q;
    FOR(i, 1, n + 1) {
        char x; cin >> x;
        if (x == '(') o[s] = ++w[p[++s] = c], c = re[i] = s;
        else if (c > 1) c = p[re[i] = c];
    }
    t.init(s);
    FOR(i, 1, s + 1) v[i].init(w[i]), t.upd(i, w[i] * (w[i] + 1) / 2);
    RFOR(i, s, 1) sz[p[i]] += ++sz[i];
    while (q--) {
        int op, l, r; cin >> op >> l >> r, l = re[l], r = re[r];
        if (op == 1) v[p[l]].upd(o[l], 1), t.upd(p[l], -w[p[l]]--);
        else {
            int x = o[r] - o[l] + 1 - v[p[l]].get(o[r]) + v[p[l]].get(o[l] - 1);
            cout << t.get(r - 1 + sz[r]) - t.get(l - 1) + x * (x + 1) / 2 << endl;
        }
    }
}